Spatial and Foveal Biases, Not Perceived Mass or Heaviness, Explain the Effect of Target Size on Representational Momentum and Representational Gravity

Abstract

The spatial memory for the last position occupied by a moving target is usually displaced forward in the direction of motion. Interpreted as a mental analogue of physical momentum, this phenomenon was coined representational momentum (RM). As momentum is given by the product of an object's velocity and mass, both these factors came to be under scrutiny in RM studies, the goal being to provide support for the internalization hypothesis. Although velocity was found to determine RM's magnitude, possible effects of mass were more elusive. Recently, an effect of target size on RM was reported, adding to previous findings that bigger targets were more mislocalized downward in the direction of gravity (via perceived heaviness and representational gravity; RG). The aim in the present research was to test that those outcomes reflect an internalization of momentum by excluding oculomotor factors. The results showed that an effect of target size, when it emerged, could be accounted for by a foveal bias such that bigger targets were more displaced toward gaze than were smaller ones. Specific contingencies between eye movements and target size seem to account for previous reports regarding the alleged effects of perceived mass on both RM and RG. This phenomenon seems furthermore to be modulated by the presence of other visual elements (fixation point) and the range of target velocities. These outcomes are taken as a rebuttal to the claim that cognitive analogues of mass or heaviness are responsible for previously reported effects of target size on both RM and RG. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

Full text

Spatial and Foveal Biases, Not Perceived Mass or Heaviness, Explain the
Effect of Target Size on Representational Momentum and
Representational Gravity
Nuno De Sá Teixeira and Armando Mónica Oliveira
University of Coimbra
The spatial memory for the last position occupied by a moving target is usually displaced forward in the
direction of motion. Interpreted as a mental analogue of physical momentum, this phenomenon was
coined representational momentum (RM). As momentum is given by the product of an object’s velocity
and mass, both these factors came to be under scrutiny in RM studies, the goal being to provide support
for the internalization hypothesis. Although velocity was found to determine RM’s magnitude, possible
effects of mass were more elusive. Recently, an effect of target size on RM was reported, adding to
previous findings that bigger targets were more mislocalized downward in the direction of gravity (via
perceived heaviness and representational gravity; RG). The aim in the present research was to test that
those outcomes reflect an internalization of momentum by excluding oculomotor factors. The results
showed that an effect of target size, when it emerged, could be accounted for by a foveal bias such that
bigger targets were more displaced toward gaze than were smaller ones. Specific contingencies between
eye movements and target size seem to account for previous reports regarding the alleged effects of
perceived mass on both RM and RG. This phenomenon seems furthermore to be modulated by the
presence of other visual elements (fixation point) and the range of target velocities. These outcomes are
taken as a rebuttal to the claim that cognitive analogues of mass or heaviness are responsible for
previously reported effects of target size on both RM and RG.
Keywords: representational momentum, representational gravity, foveal bias, eye movements, motion
perception
The concept of analog representation, along the lines of the
extended meaning given to it by Shepard (1984;Shepard & Chip-
man, 1970), has been ever since at the core of the long-standing
conjecture that, somehow, the physical principles or laws govern-
ing the outside world are internalized in our minds. As it goes, it
served as theoretical background for a series of psychophysical
phenomena, from the mental rotation paradigm (Shepard & Met-
zler, 1971) to the more recent studies on spatial mislocalizations
and, among these, representational momentum (for a review, see
Hubbard, 2005). Basically, representational momentum emerges
when an observer is shown a moving target that suddenly disap-
pears. When further asked to locate that vanishing position, ob-
servers systematically indicate a point displaced forward along the
target’s trajectory. The analogy with physical momentum (given
by the product of a projectile’s mass with its velocity) and iner-
tia—the tendency of a moving object to continue its movement—
was suggested, and the phenomenon was named after it.
Forward Displacement in Memory as an Analogue
of Physical Momentum
In the original paradigm (Freyd & Finke, 1984), participants
were shown a sequence of three rectangular shapes suggesting a
rotation movement. After this presentation, they were shown a
static rectangle, in all aspects similar to the previous ones, oriented
either in the same or a different direction of the last one seen in the
experimental sequence (mnesic probe). The task consisted in de-
ciding whether this probe was in the same or a different position
than the last one seen in the sequence (same–different paradigm).
The results showed a clear tendency to respond same for probes
further rotated along the suggested movement—as if the visual
representation of the rectangle kept rotating after the stimulus’s
disappearance. Ever since the tendency was first reported, the issue
of its potential relations with the naive physics of observers has
been a topic for research and theory. Moreover, following the
hypothesis of an internalization of momentum, the variation of
representational momentum with target velocity and acceleration
was investigated (Freyd & Finke, 1985), revealing a proportional
increase in the magnitude of displacement with the final velocity
of the target. Extending these earlier studies, representational mo-
mentum was also shown to exist for pitch (Freyd, Kelly, & DeKay,
1990), to vary with the retention interval (increasing until a peak
at about 300 ms; Freyd & Johnson, 1987), and to occur even with
static pictures imparting a sense of movement (Bertamini, 1993;
Freyd, 1983), to name just a few results.
This article was published Online First April 7, 2014.
Nuno De Sá Teixeira and Armando Mónica Oliveira, Institute of Cog-
nitive Psychology, University of Coimbra.
This work was supported by Grant SFRH/BPD/84118/2012 from the
Portuguese Foundation for Science and Technology.
Correspondence concerning this article should be addressed to Nuno
De Sá Teixeira, Institute of Cognitive Psychology, Rua do Colégio
Novo, Apartado 6153, 3001-802 Coimbra, Portugal. E-mail: nuno_
desateixeira@fpce.uc.pt
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Journal of Experimental Psychology:
Learning, Memory, and Cognition © 2014 American Psychological Association
2014, Vol. 40, No. 6, 1664–1679 0278-7393/14/$12.00 DOI: 10.1037/xlm0000011
1664

Given the independent effect of mass on physical momentum
and following the internalization hypothesis, a further test of the
momentum metaphor would rapidly follow. Cooper and Munger
(1993) measured representational momentum for the implied ro-
tation of schematic pyramids seen from above, which varied in
suggested mass (as rated by an independent group of observers).
The results did not reveal any modulation of representational
momentum’s magnitude with variations of the implied mass. This
outcome was taken as evidence that, if representational momentum
stands for an analogue of physical momentum, its internalization
does not extend to encompass the target’s mass.
During the 1990s, a significant enlargement of the study of
representational momentum was accomplished by the research of
Hubbard (see, e.g., Hubbard, 1995,1996,1997,1998,2005;Hub-
bard & Bharucha, 1988). Noteworthy in these studies were (a) the
smoothly moving stimuli that were used, instead of implied move-
ments; (b) the linear trajectory of the target’s motion, instead of
rotation; and (c) the use of a cross-shaped cursor, controlled with
the mouse, which was to be displaced to the perceived vanishing
location in order to collect participant responses (akin to the
method of adjustment; see Figure 1). The general outcomes sup-
ported the main findings reported by Freyd and collaborators.
Moreover, a whole new set of effects was unveiled. For instance,
a tendency to locate the last seen position below the movement
trajectory, together with the finding of increased displacements
forward for vertically descending targets, was interpreted as a
mental analogue of gravity, or representational gravity (Hubbard &
Bharucha, 1988). The finding of smaller displacements in memory
for objects moving in contact with surfaces was suggested to
reflect the operation of an analogue of friction, representational
friction (Hubbard, 1998). Finally, for the so-called launching effect
(Michotte, 1954), the launched target systematically presented a
reduction in representational momentum (when compared with an
isolated target moving at the same speed), which was understood
to reflect the ancient notion of impetus dissipation (Hubbard,
Blessum, & Ruppel, 2001;Hubbard & Ruppel, 2002).
These views, notwithstanding, were not without critics. As
smoothly moving targets usually engage smooth pursuit eye move-
ments (SPEM; cf. Land & Tatler, 2009), which tend to keep the
motion of the target after the target’s disappearance for at least 300
to 500 ms (Mitrani & Dimitrov, 1978), one could expect that, with
these displays, observers’ gaze overshoots the objective vanishing
location of the target. On the other hand, when performing a spatial
localization task, people show a proneness to make systematic
errors in the direction of their gaze, a phenomenon coined foveal
bias (Kerzel, 2002;Sheth & Shimojo, 2001). Despite previous
proposals that foveal bias was related with the premotor planning
of saccades (cf. Müsseler, van der Heijden, Mahmud, Deubel, &
Ertsey, 1999), it is now believed to be independent of either the
preparation or execution of eye movements and seems instead to
depend on a combination of perceptual, mnesic, and attentional
factors (Bocianski, Müsseler, & Erlhagen, 2010;Fortenbaugh &
Robertson, 2011;Sheth & Shimojo, 2001). Accordingly, we will
henceforth use the term foveal bias mainly as a descriptive label.
On the basis of these two observations (ocular overshoot and
foveal bias), Kerzel (see Kerzel, 2006, for a commentary on
Hubbard, 2005; see also Hubbard, 2006, for a reply) proposed that
representational momentum, under certain circumstances (as in the
studies conducted by Hubbard), might not reflect representational
analogues of physical properties but rather the biophysical me-
chanics and constraints of oculomotor behavior. In support of this
claim, when SPEM are constrained (e.g., by providing a fixation
point), representational momentum is suppressed (e.g., De Sá
Teixeira, Hecht, & Oliveira, 2013;Kerzel, 2000;Kerzel, Jordan, &
Müsseler, 2001). Representational friction could also be accounted
for by oculomotor behavior (Kerzel, 2002), as the presence of a
cluttered visual display reduces SPEM velocity (Collewijn &
Tamminga, 1984; a similar argument could be made regarding the
launching effect displays). The finding that representational mo-
mentum is displaced inward for circular moving targets, which was
taken to reflect a centripetal impetus (Hubbard, 1996), was later
found to be closely coupled with an ocular inward overshoot
(Kerzel, 2003). Although it is known that SPEM are sensitive to
cognitive expectations regarding the target’s motion (see, e.g.,
Krauzlis & Stone, 1999), the issue resides in drawing up the
boundaries of the degree to which a representational momentum
effect can be accounted for by an oculomotor phenomenon. That
is, an interpretation of these phenomena based on the idea of
internalized physics critically depends on showing that oculomotor
behavior is not sufficient to account for the disclosed patterns.
Be the case as it may, Hubbard’s enquiries eventually led to a
revision of the effect of suggested mass, investigated by varying
the object’s size (in light of the size–weight illusion, this manip-
ulation can, with no loss of generality, be taken as an obvious
Figure 1. Top: Standard trial for measuring the spatial displacements in
memory for moving targets. Bottom: Measurement of spatial displace-
ments. The black squares depict the objective vanishing location for targets
moving leftward, rightward, upward, and downward, as represented by the
gray arrows. White and dashed squares represent the usual judged vanish-
ing points. Full and dashed lines indicate, respectively, the measurement
axes for M- and O-displacements. M-displacement ⫽mislocalization along
the target’s trajectory (M ⫽motion axis); O-displacement ⫽errors along
the axis orthogonal to the target’s trajectory (O ⫽orthogonal axis).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1665
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

manipulation of implied mass). In partial agreement with the result
of Cooper and Munger (1993), no effect was found in the forward
displacement with horizontally moving stimuli, although an effect
of target size on the downward displacement for both vertical and
horizontal movements (i.e., displacements aligned with the direc-
tion of gravity) was reported (Hubbard, 1995,1997). According to
Hubbard, it appears that mass needs to operate as a weight, through
its phenomenological consequences in a world of gravity, in order
to have an effect on the magnitude of spatial displacements. Rather
than viewing it as an effect of mass per se, this hypothesis views
it as an instance of the subjectively experienced weight (Hubbard,
2005), the implication being that the representation of the physical
world is accomplished by a second-order isomorphism with the
experienced effects and not through an internalization of the ob-
jective kinematic and/or dynamic properties (Hubbard, 2005; see
also Shepard & Chipman, 1970). The theory-neutral expression
forward displacement was accordingly favored by Hubbard over
the more theory-laden representational momentum designation.
Moreover, in order to gauge the mnesic spatial displacements
when using behavioral localization methods, the M- and
O-displacements were suggested as measures (cf. Hubbard,
2005). M-displacement refers to the mislocalization made along
the target’s trajectory (with Mstanding for motion axis), and
O-displacement refers to the errors along the axis orthogonal to
the target’s trajectory (with Ostanding for orthogonal axis; see
Figure 1).
Reappraisal of the Effect of Implied Mass
Given the relevance of an effect of the target’s perceived mass
for the hypothesis of an internalization of momentum, it is note-
worthy that few studies have addressed such an effect. In this line
of reasoning and following the momentum metaphor, studies con-
ducted in our laboratory have come to show that target size does
indeed modulate the magnitude of representational momentum. De
Sá Teixeira, Oliveira, and Simões (2010) first obtained an in-
creased representational momentum proportional to target size (the
stimuli being black squares moving on an otherwise white back-
ground). The fact that targets moved at slightly faster speeds
(between 5.73 and 17.1°/s) than in Hubbard’s 1997 experiments
(between 2.5 and 7.5°/s) might account for the disparate results.
This finding was later replicated in De Sá Teixeira, de Oliveira,
and Amorim (2010) with textured spheres of varying sizes. Fi-
nally, De Sá Teixeira, Pimenta, and Raposo (2013) reported an
effect of target size on representational momentum for both normal
controls and patients with schizophrenia, although the latter were
shown to be insensitive to target velocity. This outcome was taken
to reflect the known deficits in SPEM displayed by patients with
schizophrenia (see, e.g., Chen, 2011, for a review). This study thus
suggests that the found increased representational momentum for
larger targets might not be due to a smooth pursuit overshoot.
The present paper aims to assess the degree to which the size of
moving targets leads to patterns of mislocalizations that can be
substantively interpreted as internalized physical notions of an
object’s mass and/or heaviness. In order to do so, we will cover the
entire range of situations that have been previously reported to be
sensitive to target size, such as forward displacement with hori-
zontally moving targets (Experiments 1 and 2), downward dis-
placement with horizontally moving targets (Experiments 2a and
2b), and forward displacement with vertically moving targets
(where the result of interest is focused on the comparison between
ascending and descending targets; Experiments 3 and 4). The role
of oculomotor factors will be investigated both by constraining and
measuring the gaze patterns (Experiments 1 and 3).
Experiment 1: Exploring the Effect of Target Size
on Horizontally Moving Targets While Controlling
Eye Movements
Our purpose in this first experiment was to directly ascertain the
role of SPEM in the effect of target size on forward displacement
given horizontally moving targets (representational momentum).
Our hypothesis was that constraining SPEM would not compro-
mise the proportional increase in the forward displacement with
variations of target size. In order to do so, we showed targets
varying in size and velocity to observers instructed either to fixate
a static point or to freely follow the targets with their eyes, in a
counterbalanced order. If target size is unrelated with oculomotor
factors, its effect would emerge irrespective of eye movement
instructions.
Method
Participants. Fourteen students of the University of Coimbra
(13 female, 1 male) volunteered for the experiment in exchange for
partial course credit. Their ages ranged from 18 to 23 years (M⫽
18.8, SD ⫽1.37). All of them had normal or corrected to normal
vision and were unaware of the purposes of the experiment.
Stimuli. A set of animations was used as stimuli. Each ani-
mation depicted a black square (target), 30, 60, or 90 pixels (px)
wide (⬇.9°, 1.8°, or 2.75°), moving horizontally at a constant
speed of 150, 300, or 450 pixels per second (px/s; 4.6, 9.2, or
13.7°/s). The target’s path was vertically centered on the screen. A
black dot (fixation point), 5 px (⬇.15°) in diameter, was shown
during each animation 60 pixels (⬇1.8°) below the target’s trajec-
tory and centered horizontally on the screen. Both the target and
the fixation dot were shown on an otherwise white background.
The targets appeared already in motion 390, 410, or 430 px
(⬇11.9, 12.5, or 13.1°) to the left (for rightward movements) or to
the right (for leftward movements) of the center of the screen and
disappeared after covering a total distance of 500 px (⬇15.2°); that
is, 110, 90, or 70 px (⬇3.4, 2.8, or 2.1°) beyond the center of the
screen. The target and the fixation dot vanished simultaneously.
Procedure and design. The experiment was run on a personal
computer equipped with a 17-in. flat screen (physical size of 34 ⫻
27.3 cm; 37.5 ⫻30.5°) with resolution 1,280 ⫻1,024 px and a
refresh rate of 60 Hz. The participant’s head was constrained with
a chin rest such that the participant’s cyclopean eye was aligned
with the center of the screen at a fixed distance of 50 cm. An eye
tracker (Arrington Research, PC-60) was attached to the chin rest,
and the participant’s eye movements were monitored (glint-pupil
vector method at 60 Hz) during the entire experiment. Each par-
ticipant completed two tasks in a counterbalanced order. In one
task and for each trial, participants were instructed to maintain
their gaze on the fixation dot as long as it was present on the screen
(henceforth referred to as constrained eye movements task or
simply CM). In the other task, they were free to follow the target
with their eyes (smooth pursuit task or SP). Except for the eye
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1666 DE SÁ TEIXEIRA AND OLIVEIRA

movement instructions, both tasks were in all respects alike. Each
trial started with the presentation of the fixation dot alone until the
participant acknowledged that she or he was ready to watch
the next animation by pressing the left button of an optical mouse.
The target appeared in motion immediately afterward, and, after it
disappeared, participants were instructed to locate, as precisely as
possible and referring to the geometrical center, its vanishing
location. In order for them to do so, after the end of each anima-
tion, a plus-shaped cursor, controllable with the mouse, appeared
on the center of the screen. Participants were required to move the
cursor with the mouse to the desired location and to confirm each
response by pressing the mouse’s left button. The experiment
followed a full factorial repeated measures design given by 3
(target velocity) ⫻3 (target size) ⫻3 (vanishing position) ⫻2
(movement direction) ⫻2 (task: SP and CM). Each animation was
shown three times per task, thus resulting in a total of 324 trials.
The entire experiment lasted about 50 minutes including instruc-
tions, an intertask interval, and the debriefing.
Results
Due to technical reasons, the results of one participant in the SP
task were lost. For the remaining participants, the arithmetic dif-
ference between the horizontal objective vanishing location of the
target onscreen and the participant’s response (M-displacement)
was calculated for each trial in pixels. Likewise, the difference
between the vertical objective vanishing location on the screen and
the participant’s response (O-displacement) was calculated. Neg-
ative numbers in M-displacement index a remembered vanishing
position behind the objective location where the target disappeared
(in relation to its motion direction), and positive numbers reflect a
forward displacement. Likewise, negative O-displacement values
indicate a remembered vanishing location below the objective
position, and positive numbers refer to a location above (see Figure
1). The data thus obtained were averaged across replications and
subjected to two repeated measures analyses of variance (ANOVAs),
one for each component (M- and O-displacement). A main effect
of eye movement instructions (SP or CM task) was found on the
overall magnitude of M-displacement, F(1, 12) ⫽140.94, p⬍
.001, partial ␩
2
⫽.92, and O-displacement, F(1, 12) ⫽389.5, p⬍
.001, partial ␩
2
⫽.97. Moreover, for M-displacement, eye move-
ment instructions was found to interact with target velocity, F(2,
24) ⫽11.16, p⬍.001, partial ␩
2
⫽.48; size, F(2, 24) ⫽9.9, p⫽
.001, partial ␩
2
⫽.45; and vanishing position, F(2, 24) ⫽8.16,
p⫽.002, partial ␩
2
⫽.4. With no eye movements allowed (CM
task), M-displacement was negative and faster targets failed to
result in a bigger M-displacement, in contrast with the SP condi-
tion. Conversely, bigger targets led to less M-displacement in the
CM task but had no effect on the SP task. Finally, targets that
disappeared farther beyond the center of the screen were shown to
result in less M-displacement and more so when eye movements
were constrained. On the basis of these results, separate analyses
were conducted for the SP and CM tasks.
Smooth pursuit task. The mean gaze location during each
trial was averaged across replications, direction, and vanishing
locations. Figure 2 presents horizontal gaze location (in pixels and
in reference to the target’s motion direction, with 0 being the
vanishing location) as a function of time (from 500 ms before to
500 ms after the target vanished; 0 is the moment when the target
disappeared) for the different target velocities (panel A) and sizes
(panel B). It can be seen that participants’ gaze smoothly pursued
the target (dotted lines) while it was in motion. When the target
vanished, participants’ gaze kept its motion for at least 200 ms
before stabilizing. The magnitude of the ocular overshoot clearly
depends on target velocity (between about 25 and 75 px beyond
the vanishing point) but is unchanged by its size. Vertical gaze
location was roughly constant while the target was visible but
drifted slightly downward after its disappearance, with no differ-
ences for the different velocities or sizes. This trend can be seen in
Figure 3, which depicts vertical gaze position (in regard to the
vanishing point) as a function of normalized response times (for
each trial and with 1 being the moment when a response was given,
so as to account for differences in response times).
Figure 4 presents the mean M- (panels A and B) and
O-displacements (panels C and D) as a function of target velocity
Figure 2. Mean horizontal gaze locations as a function of time (.5 s before and after target’s disappearance),
target’s velocity (panel A, line parameters), and target size (panel B, line parameters) in the SP task of
Experiment 1. Notice that the ordinate represents gaze position in reference to target’s trajectory (dotted line),
so that negative numbers refer to gaze locations behind the vanishing location of the target (smooth pursuit) and
positive numbers refer to locations beyond (overshoot). SP ⫽smooth pursuit; px ⫽pixels.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1667
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

(panels A and C) and size (panels B and D). It can be seen that
faster targets lead to significantly bigger M-displacements, F(2,
24) ⫽27.5, p⬍.001, partial ␩
2
⫽.7; linear contrast: F(1, 12) ⫽
37.62, p⬍.001, partial ␩
2
⫽.76. Target size, however, had no
effect on the mean M-displacement, F(2, 24) ⫽2.22, p⫽.13. The
location on screen where the target vanished significantly modu-
lated the magnitude of M-displacement, F(2, 24) ⫽10.5, p⫽.001,
partial ␩
2
⫽.5; linear contrast: F(1, 12) ⫽13.85, p⫽.003, partial
␩
2
⫽.54, in agreement with previously reported results (De Sá
Teixeira & Oliveira, 2011). That is, targets that covered bigger
distances after crossing the screen’s midpoint resulted in less
M-displacement (70-px condition: M⫽33.24 px, SD ⫽15.6;
90-px condition: M⫽28.6 px, SD ⫽16.35; 110-px condition:
M⫽25.64 px, SD ⫽17.82).
As for O-displacement, target size, F(2, 24) ⫽7.9, p⫽.002,
partial ␩
2
⫽.4; linear contrast: F(1, 12) ⫽8.35, p⫽.014, partial
␩
2
⫽.41, but not velocity, F(2, 24) ⫽1.5, p⫽.25, significantly
affected its mean magnitude, with bigger targets leading to a
bigger displacement downward. No other effects were statistically
significant.
Constrained eye movements task. Trials where participants’
gaze fell outside a region of interest of 30 pixels around the
fixation point while it was present on screen were discarded in this
task. These amounted to 2.25% of trials. For the remaining trials,
M- and O-displacements were calculated as before. Figure 4 pres-
ents the obtained results as a function of target velocity and size
(respectively, left and right column, dashed lines).
Overall, M-displacement was negative for this condition (Figure
4, panels A and B); that is, the remembered vanishing location was
systematically behind the objective vanishing position. In contrast
with the outcomes of the SP task, size, F(2, 26) ⫽16, p⬍.001,
partial ␩
2
⫽.55; linear contrast: F(1, 13) ⫽22.68, p⬍.001,
partial ␩
2
⫽.64, but not velocity, F(2, 26) ⬍1, significantly
modulated M-displacement. Of importance, bigger targets resulted
in less M-displacement than did smaller ones. The target’s van-
ishing point was also shown to be significant, F(2, 26) ⫽29.8, p⬍
.001, partial ␩
2
⫽.7; linear contrast: F(1, 13) ⫽55.34, p⬍.001,
partial ␩
2
⫽.81, replicating the trend previously found (70-px
condition: M⫽⫺8.8 px, SD ⫽12.4; 90-px condition: M⫽⫺17.2
px, SD ⫽15.1; 110-px condition: M⫽⫺23.9 px, SD ⫽17.2). For
the O-displacement (Figure 4, panels C and D), only target size,
F(2, 26) ⫽5.3, p⫽.01, partial ␩
2
⫽.3; linear contrast: F(1, 13) ⫽
6.1, p⫽.028, partial ␩
2
⫽.32, influenced its magnitude, with
bigger targets resulting in bigger displacements downward.
Discussion of Experiment 1
Experiment 1 aimed at replicating the previously reported effect
of target size on M-displacement, where bigger targets were shown
to result in higher M-displacements (De Sá Teixeira, de Oliveira,
& Amorim, 2010;De Sá Teixeira, Oliveira, & Simões, 2010;De
Sá Teixeira, Pimenta, & Raposo, 2013). The obtained outcomes
failed to replicate that effect. Instead, we obtained the exact
inverse pattern and only when participants’ gaze was constrained.
That is, under that condition, the remembered vanishing location
of bigger targets was more displaced backward in comparison with
smaller targets. Gaze location, which was behind the objective
vanishing location in the CM task, seems to be the determining
factor: Bigger targets were mislocalized further in the direction of
gaze than smaller ones. Said another way, target size appears to
modulate the magnitude of foveal bias. This finding is in accor-
dance with the results reported by Müsseler et al. (1999), where
stimuli that encompassed bigger spatial extents were more sub-
jected to foveal bias.
Conversely, when participants were free to move their eyes, no
effect of target size emerged, despite the presence of an ocular
Figure 4. M- (panels A and B) and O-displacements (panels C and D) as
a function of velocity (abscissa of panels A and C) and size (abscissa of
panels B and D) for both the SP task (full lines and black circles) and the
CM task (dashed lines and white circles) in Experiment 1. Error bars
indicate standard errors of the mean. M-displacement ⫽mislocalization
along the target’s trajectory (M ⫽motion axis); O-displacement ⫽errors
along the axis orthogonal to the target’s trajectory (O ⫽orthogonal axis);
SP ⫽smooth pursuit; CM⫽constrained eye movements; px ⫽pixels.
Figure 3. Mean vertical gaze position in the SP task of Experiment 1, in
reference with the target’s vanishing point (0 in the ordinate), as a function
of normalized response times (0 is the moment when a response was
provided). SP ⫽smooth pursuit; px ⫽pixels.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1668 DE SÁ TEIXEIRA AND OLIVEIRA

overshoot. This finding is at odds with previous outcomes reported
by our team (De Sá Teixeira, de Oliveira, & Amorim, 2010;De Sá
Teixeira, Oliveira, & Simões, 2010;De Sá Teixeira, Pimenta, &
Raposo, 2013). The fact that, in this study and even in the SP task,
a fixation point was present during each trial might account for this
disparate outcome. It is possible that the presence of a fixation dot
acts as a fixed spatial reference that anchors the remembered
vanishing location. In fact, Sheth and Shimojo (2001) reported a
similar observation when studying foveal bias: Although the pres-
ence or absence of a fixation point does not change foveal bias
when eye movements are not allowed, the presence of a salient
visual reference in the display with no eye constraints seems to
lead to similar spatial mislocalizations (toward the irrelevant visual
element). It thus follows that foveal bias might be but a particular
instance of a systematic proneness to mislocalize objects toward a
fixed frame of reference, be it observer’s gaze or a salient visual
element.
Be the case as it may, our results did replicate Hubbard’s
(1997;Hubbard & Bharucha, 1988) finding that targets are
remembered as being below their objective vanishing location
and that the magnitude of this downward displacement in-
creases for bigger targets. Of importance, this trend emerged
both when participants could follow the target with their eyes
and when gaze was constrained. However, as the gaze position
in the SP task was shown to drift downward while the partici-
pants were providing their spatial judgments (for a similar
outcome see De Sá Teixeira, Hecht, & Oliveira, 2013), the
increased downward displacement for bigger targets is also
compatible, in this case, with a foveal bias. Notice, however,
that the location of the fixation dot below the target’s path,
acting as a fixed spatial reference, might as well be argued to be
responsible for the effect of target size on O-displacement. At
this moment, both a spatial bias (be it due to gaze location or the
fixation point) and an interpretation in terms of perceived
heaviness could account for the observed O-displacement
trends.
Experiment 2: Exploring the Representational
Trajectory of Horizontally Moving Targets With
Varying Sizes
This next experiment attempted to again replicate the findings
reported by our laboratory by presenting the targets without the
fixation point. Furthermore, to explore a possible role of the
perceived heaviness of the targets in O-displacement, we imposed
retention intervals between the target disappearance and the par-
ticipant’s response, building upon previous results that show that
the remembered vanishing location of a moving target drifts down-
ward in the direction of gravity with time in a representational
trajectory (De Sá Teixeira, Hecht, & Oliveira, 2013). According to
Hubbard’s proposal, bigger targets are further mislocalized down-
ward because they are perceived as heavier. It is legitimate to
hypothesize that, if such is the case, the temporal profile of this
downward drift could be modulated by target size and be observ-
able in the dynamics of representational trajectory. For instance, it
might be that bigger targets, perceived as heavier, drift downward
at an increased rate.
We thus predicted that (a) given the absence of a fixation point,
bigger targets would lead to bigger displacements in the direction
of motion; (b) bigger targets would be further displaced down-
ward; and (c) the remembered vanishing location would change
differently with time for bigger targets.
Experiment 2a
Method
Participants. Twenty-two new students of the University of
Coimbra (19 female, 3 male), with ages between 18 and 30 years
(M⫽18.9, SD ⫽2.53), volunteered for the experiment in ex-
change for partial course credit. All of them had normal or cor-
rected to normal vision and were unaware of the purposes of the
task.
Stimuli. The set of animations from Experiment 1 was used as
stimuli. However, no fixation point was present during the target’s
movement, and only two vanishing locations were used (70 and
110 pixels beyond the screen’s midpoint). A retention interval of
0, 150, 300, 450, or 600 ms was imposed after the disappearance
of the target and before the plus-shaped cursor was shown.
Procedure and design. The procedure was identical to the
one followed in Experiment 1 (SP task) except for the following:
Neither eye nor head movements were constrained, but partici-
pants were instructed to maintain a steady posture (at about 50
centimeters from the screen) during the entire experiment. Like-
wise, eye movements were not monitored. As in Experiment 1,
participants were instructed to indicate, as precisely as possible
and referring to the geometrical center of the target, the target’s
vanishing location onscreen. Furthermore, they were instructed to
wait until the cursor was shown before providing their answers.
The experiment thus followed a full factorial repeated measures
design given by 3 (target velocity) ⫻3 (target size) ⫻2 (vanishing
location) ⫻2 (movement direction) ⫻5 (retention interval) with
two replications, thus amounting to 360 trials. The entire experi-
ment, including instructions and debriefing, lasted about 45 min-
utes.
Results
M- and O-displacements were calculated as in Experiment 1,
and the data obtained were likewise subjected to two repeated
measures ANOVAs.
Both target velocity, F(2, 42) ⫽20.63, p⬍.001, partial ␩
2
⫽
.49; linear contrast: F(1, 21) ⫽24.98, p⬍.001, partial ␩
2
⫽.54,
and size, F(2, 42) ⫽41.25, p⬍.001, partial ␩
2
⫽.66; linear
contrast: F(1, 21) ⫽48.82, p⬍.001, partial ␩
2
⫽.7, significantly
determined M-displacement’s magnitude. Overall, both bigger and
faster targets led to significantly higher values of M-displacement.
Significant effects of vanishing point, F(1, 21) ⫽107.27, p⬍.001,
partial ␩
2
⫽.8; linear contrast: F(1, 21) ⫽107.27, p⬍.001, partial
␩
2
⫽.84, and retention time, F(4, 84) ⫽10.29, p⬍.001, partial ␩
2
⫽
.33; quadratic contrast: F(1, 21) ⫽20.46, p⬍.001, partial ␩
2
⫽.49,
were also found. Targets that vanished farther beyond the center of the
screen resulted in smaller M-displacements (70-px condition: M⫽
29.9 px, SD ⫽18.84; 110-px condition: M⫽22.1, SD ⫽17.75).
As for retention interval, it was found to also interact with velocity,
F(8, 168) ⫽8.22, p⬍.001, partial ␩
2
⫽.28; with a significant
quadratic-linear contrast: F(1, 21) ⫽23.68, p⬍.001, partial ␩
2
⫽
.53, in a pattern where M-displacement increased with time and
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1669
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

increasingly so for faster targets, until a maximum at about 150 to
300 ms. No other effect was found to be significant.
For O-displacement, target velocity, F(2, 42) ⫽4.95, p⫽.012,
partial ␩
2
⫽.19; linear contrast: F(1, 21) ⫽9.65, p⫽.005, partial
␩
2
⫽.32; size, F(2, 42) ⫽4.93, p⫽.012, partial ␩
2
⫽.19; linear
contrast: F(1, 21) ⫽5.26, p⫽.032, partial ␩
2
⫽.2; vanishing
position, F(1, 21) ⫽8.33, p⫽.009, partial ␩
2
⫽.28; linear
contrast: F(1, 21) ⫽8.33, p⫽.009, partial ␩
2
⫽.28; and retention
time, F(4, 84) ⫽9.73, p⬍.001, partial ␩
2
⫽.32; linear contrast:
F(1, 21) ⫽21.22, p⬍.001, partial ␩
2
⫽.5, were statistically
significant. No interactions were found. In general, O-displacement
increased downward, with increases in retention time and vanishing
locations further beyond the center of the screen. Bigger targets
resulted in an overall bigger displacement upward than did smaller
ones. Finally, there was a slight tendency for faster targets to be
remembered as displaced upward.
Figure 5 depicts these outcomes (continuous lines and black
markers). In contrast with both the findings of Experiment 1 and
Hubbard’s reports, the effect of target size on O-displacement was
reversed: Whereas bigger targets were previously found to be
further displaced downward, in the present experiment O-displacement
actually increased upward for bigger targets (see Figure 5, panel C).
Although the presence of a fixation dot in our first experiment
might account for this divergence, the same cannot be said regard-
ing Hubbard’s data, where no fixation point was ever present.
Notwithstanding, the velocities used in the present experiment
(4.6, 9.2, or 13.7°/s) are overall faster than the ones used by
Hubbard (1997; between 2.5 and 7.5°/s). In order to ascertain if
this methodological difference could account for the disparate
findings, we replicated the present experiment with slower moving
targets.
Experiment 2b
Method
Participants. Nineteen new participants (15 female, 4 male)
with ages between 18 and 29 years (M⫽21.32, SD ⫽4.46) were
recruited for Experiment 2b.
Stimuli. A set of animations in all regards similar to the ones
in Experiment 2a was used as stimuli, with the exception of the
moving velocities, which could be 75, 150, or 225 px/s (⬇2.3, 4.6,
or 6.9°/s).
Procedure and design. The procedure of Experiment 2a was
adopted in Experiment 2b, and an equivalent design was em-
ployed.
Results
As in Experiment 2a, target velocity significantly determined
the magnitude of M-displacement, F(2, 36) ⫽5.38, p⫽.009,
partial ␩
2
⫽.23; linear contrast: F(1, 18) ⫽6.22, p⫽.023, partial
␩
2
⫽.26, with faster targets resulting in a bigger displacement in
the direction of motion. On the other hand, neither target size, F(2,
Figure 5. M- (panels A and B) and O-displacements (panels C and D) as a function of time (abscissas), target’s
velocity (panels B and D), and size (panels A and C) for Experiments 2a (black markers and full lines) and 2b
(white markers and dashed lines). Error bars indicate standard errors of the mean. M-displacement ⫽mislo-
calization along the target’s trajectory (M ⫽motion axis); O-displacement ⫽errors along the axis orthogonal
to the target’s trajectory (O ⫽orthogonal axis); Exp. ⫽experiment; px ⫽pixels.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1670 DE SÁ TEIXEIRA AND OLIVEIRA

36) ⫽2.12, p⫽.105, nor retention interval, F(4, 72) ⬍1, had an
effect on M-displacement. For O-displacement, both target veloc-
ity, F(2, 36) ⫽14.9, p⬍.001, partial ␩
2
⫽.45; linear contrast:
F(1, 18) ⫽24.85, p⬍.001, partial ␩
2
⫽.58, and retention
interval, F(4, 72) ⫽12.17, p⬍.001, partial ␩
2
⫽.4; linear
contrast: F(1, 18) ⫽28.83, p⬍.001, partial ␩
2
⫽.62, were
significant, with slower targets and longer retention intervals re-
sulting in a bigger displacement downward. The effect of target
size was only marginally significant in determining the magnitude
of O-displacement, F(2, 36) ⫽2.8, p⫽.074, partial ␩
2
⫽.14. This
trend was mostly due to the biggest target (90 px
2
), which was
further mislocalized downward. No other effect or interaction was
significant.
Figure 5 shows the outcomes of Experiments 2a (black markers
and continuous lines) and 2b (white markers and dashed lines).
Panels A and B depict the mean M-displacements, and panels C
and D depict the mean O-displacements. Data are plotted as a
function of retention interval (abscissas; in milliseconds), target
sizes (panels A and C, line parameters), and velocities (panels B
and D, line parameters).
Discussion of Experiments 2a and 2b
Overall, in both experiments, the remembered vanishing loca-
tion was displaced forward in the direction of motion (represen-
tational momentum), and the magnitude of this displacement in-
creased with target velocity. However, it is worth noticing that
target velocity does not invariably lead to the same amount of
M-displacement, rather being modulated by the range of velocities.
For instance, in both experiments some targets were shown mov-
ing at a constant velocity of 150 px/s (Level 1 in Experiment 2a;
Level 2 in Experiment 2b). Notwithstanding, the magnitude of
M-displacement for this particular velocity varies between exper-
iments (22.34 px in Experiment 2a and 7.46 px in Experiment 2b).
This variation might signal a contextual effect in representational
momentum, although it is still to be determined if it impacts on the
kinematics of the internal representation or at the level of the
oculomotor pursuit.
With increases in target size, there was but a slight tendency to
remember the vanishing position further displaced downward, in
Experiment 2b. The inverse trend was disclosed in Experiment 2a.
This result disproves that, with no fixation point, target size
unambiguously determines O-displacement, and, when it does, it
seems to depend on the range of target velocities. Our results thus
fail to support that the patterns of spatial mislocalizations are
sensitive to the perceived target’s heaviness. This point seems to
be further reinforced by the absence of an interaction between
target size and retention interval. In both Experiments 2a and 2b
we replicate the finding that the remembered vanishing location of
a moving target drifts downward in the direction of gravity with
time (representational trajectory; De Sá Teixeira, Hecht, & Ol-
iveira, 2013). Although a specific prediction regarding the tempo-
ral pattern for targets perceived as heavier cannot be unambigu-
ously made based solely on Hubbard’s suggestion, we hypothesized
that the rate of the downward drift would be higher for targets
perceived as heavier. We found no evidence for such trend. In fact,
target size did not modulate in any way the representational
trajectory. In order to further explore this point, the slope of the
best linear fit between retention interval and O-displacement was
calculated on an individual basis for each target size in both
Experiments 2a and 2b. The slope of the linear fit indexes the rate
at which the spatial memory drifts downward (cf. De Sá Teixeira,
Hecht, & Oliveira, 2013). Target size had no effect in Experiment
2a, F(2, 2) ⫽1.65, p⫽.2, or Experiment 2b, F(2, 2) ⬍1, although
the rate of downward displacement was systematically different
from 0 (p⬍.01 for all sizes in both experiments). Furthermore, the
rate of the downward drift was not significantly different between
Experiment 2a (M⫽⫺2.4 px/s; SD ⫽2.5) and Experiment 2b
(M⫽⫺4.1 px/s; SD ⫽3.3), F(2, 78) ⬍1 (see Figure 5, panels C
and D). The remembered vanishing location drifted downward
with time at a constant rate of about 3.25 px/s in both experiments
and for all sizes. It might be argued that, as participants necessarily
take some time to provide their answers, one has to consider not
only the manipulated retention intervals but also the response
times. However, although observers showed a systematic tendency
to respond faster when given longer delays after stimulus offset
(Experiment 2a: F(2.59, 54.4) ⫽61.19, p⬍.001, partial ␩
2
⫽.74;
Experiment 2b: F(2.73, 49.15) ⫽24.85, p⬍.001, partial ␩
2
⫽
.58), we found no evidence of a correlation between response
times and the magnitude of M- or O-displacement. Also, the trend
uncovered for the response times did not change the monotonic
order of the retention intervals (in Experiment 2a, mean response
times were 1,905, 1,795, 1,742, 1,690, and 1,689 ms for the 0-,
150-, 300-, 450-, and 600-ms retention intervals, respectively; in
Experiment 2b, the mean response times for the same conditions
were 2,146, 2,078, 1,984, 1,995, and 1,900 ms), and thus, if
anything, this trend affects only the downward drift rate. If such is
the case, our reported value of 3.25 px/s might actually be under-
estimated.
Finally, we did replicate previous findings from our laboratory
where M-displacement was shown to increase for bigger targets,
although this effect too seems to depend on the range of velocities,
as it emerged in Experiment 2a but not in Experiment 2b. Con-
trasting the outcomes of Experiment 2a with the ones disclosed in
Experiment 1 (SP task), we can now also qualify the effect of
target size as dependent on the presence or absence of a fixation
point. That is, the presence of a visual spatial reference onscreen
prevents the increase in M-displacement that would otherwise be
observed for bigger targets. Of importance, however, this outcome
further strengthens the conclusion that the found effects of target
size on the spatial mislocalizations (both M- and O-displacements)
might depend on a spatial bias, rather than on a cognitive inter-
nalization of physical mass and/or heaviness. Given the foveal bias
found in the CM task in Experiment 1, together with the ocular
overshoot that emerges when no eye constraints are imposed (SP
task in Experiment 1), we surmise that in the present experiment,
as well as in previous ones (De Sá Teixeira, de Oliveira, &
Amorim, 2010;De Sá Teixeira, Oliveira, & Simões, 2010;De Sá
Teixeira, Pimenta, & Raposo, 2013), the effect of target size in
M-displacement is due to the fact that, when participants provide
the spatial judgment, their gaze lies beyond the vanishing location
of the target. If bigger targets are indeed further mislocalized
toward gaze, it follows that an increase in M-displacement pro-
portional with target size would be the case given an ocular
overshoot. The mere presence of an extraneous visual element,
such as a fixation point, seems to disrupt these trends, at least when
located behind the target’s vanishing location (SP condition in
Experiment 1).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1671
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

Irrespective of the ultimate explanation for these outcomes, our
findings are clearly more unfavorable than not to an interpretation
in terms of perceived objects’ mass or heaviness. Instead, the
pattern of results seems to be revealing some effects of foveal and
spatial biases in the behavioral localizations, at least for horizon-
tally moving targets.
As for vertically moving targets, by virtue of being aligned with
the gravitational pull, we can hypothesize that additional mecha-
nisms (e.g., representational gravity; cf. Hubbard, 2005) might be
triggered and that our conclusions so far do not generalize to such
displays. The remaining experiments focus on vertically moving
targets in order to ascertain this hypothesis.
Experiment 3: Exploring the Effect of Target Size
on Vertically Moving Targets While Controlling
Eye Movements
Although the found effects of target size on spatial mislocaliza-
tions of horizontally moving targets seem to be modulated by
foveal and spatial biases, the possibility still remains that even
though perceived heaviness does not seems to determine
O-displacement, it might modulate M-displacement when the tar-
gets are shown moving vertically. Hubbard (1997) found that
bigger targets result in bigger displacements in the direction of
motion for descending objects but in a decreased displacement for
ascending objects, a result that was interpreted as evidence for a
cognitive analogue of mass or rather its expected heaviness.
Experiment 3 aims at ascertaining the degree to which the found
effects of target size on spatial mislocalizations generalize for
cases where the object’s motion explicitly unfolds along the grav-
itational axis. Given previous evidence that representational mo-
mentum is sensitive to the physical direction of gravity (being
increased for motions toward the gravity pull; Hubbard, 1997;
Nagai, Kazai, & Yagi, 2002), it can be argued that the perceived
heaviness of targets modulates forward displacements only with
vertically moving targets. This hypothesis would be compatible
with Hubbard’s proposal (Hubbard, 1997,2005) that an effect of
dynamic characteristics of objects, such as mass, requires a phe-
nomenological consequence (through perceived heaviness) to sig-
nificantly affect representational momentum. It is important to
notice that this hypothesis is not incompatible with an effect of
foveal and/or spatial biases; the two bias types could jointly
determine the magnitude of spatial displacements. The critical
manipulation to disentangle these disparate effects resides in con-
straining the eye movements: It might be the case that, if the
participant’s gaze is fixed behind the vanishing location, bigger
targets are localized toward the foveated position (as in the CM
condition of Experiment 1) by differing amounts for ascending as
compared to descending motions. The ensuing prediction is that
with constrained eye movements, a significant interaction between
motion direction and target size would result. In contrast, if bigger
targets are mislocalized toward gaze by equal amounts for both
ascending and descending movements (indexed by a null interac-
tion), such would be further evidence against the proposal that
perceived heaviness modulates representational momentum.
Method
Participants. Ten new students of the University of Coimbra
(2 male, 8 female), with normal or corrected to normal vision and
ages between 18 and 23 years (M⫽18.9, SD ⫽1.52), volunteered
for the experiment in exchange for partial course credit.
Stimuli. A set of animations similar to that used in Experi-
ment 1 was used as stimuli, with the following exceptions. Only
one target velocity was used (300 px/s). The targets could move
upward or downward and disappeared 70, 90, or 110 pixels after
crossing the center of the screen. A fixation dot was present during
the animation 60 pixels to the left of the target’s path and centered
vertically on the screen.
Procedure and design. The procedure and apparatus were in
all respects similar to those used in Experiment 1. The experiment
followed a full factorial repeated measures design given by 3
(target size) ⫻2 (motion direction: upward or downward) ⫻3
(vanishing location on screen) ⫻2 (task: SP and CM) with three
repetitions, thus amounting to 108 trials. The entire experiment
lasted about 30 minutes, including instructions, debriefing, and an
intertask interval.
Results
M- and O-displacements were calculated as in the previous
experiments. Notice, however, that here M-displacement refers to
localization errors aligned with the vertical (i.e., with both target’s
movement and gravity), while O-displacement indexes horizontal
errors (orthogonal to both target’s motion and gravity). The data
obtained were subjected to two repeated measures ANOVAs, one
for each component (M- and O-displacement). Eye movement
instructions had a significant effect on the magnitude of
M-displacement, F(1, 9) ⫽25.16, p⫽.001, partial ␩
2
⫽.74, as
well as significant interactions with target size, F(2, 18), 7.46, p⫽
.004, partial ␩
2
⫽.45; motion direction, F(1, 9) ⫽6.52, p⫽.031,
partial ␩
2
⫽.42; and vanishing location, F(2, 18) ⫽93.57, p⬍
.001, partial ␩
2
⫽.91. M-displacement was negative (behind the
objective vanishing location) for the CM condition but positive for
the SP condition. Furthermore, contrary to the SP task, bigger
targets led to a smaller M-displacement in the CM condition.
When the targets covered a greater distance beyond the center of
the screen, M-displacement was decreased and more so when eye
movements were not allowed. As for O-displacement, eye move-
ment instructions was found to have a significant main effect, F(1,
9) ⫽196.13, p⬍.001, partial ␩
2
⫽.96, as well as significant
interactions with target size, F(2, 18) ⫽10.6, p⫽.001, partial
␩
2
⫽.54, and vanishing location, F(2, 18) ⫽6.37, p⫽.008,
partial ␩
2
⫽.41. In the CM condition, spatial memory was
generally biased leftward toward the gaze location and by a greater
amount for bigger targets. In the SP condition, the memory for the
location of bigger targets was slightly more displaced leftward
(toward the fixation dot) but only for descending motions. In light
of these results, separate analyses were conducted for the SP and
CM tasks.
Smooth pursuit task. Figure 6 depicts the mean vertical gaze
locations as a function of time in the SP task. Panel A shows the
gaze positions (in relation to the target’s motion direction) from
500 ms before and after the target disappearance (0 in the time
axis). It can be seen that participants tended to smoothly pursue the
target (dotted line) while it was shown. Furthermore, for both
downward- and upward-moving targets, the participant’s gaze
continued to move after the target vanished for at least 200 ms,
overshooting that location by about 45 pixels. Panel B shows the
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1672 DE SÁ TEIXEIRA AND OLIVEIRA

mean vertical gaze locations after the disappearance of the target
against normalized response time (on a trial by trial basis and so as
to account for the variable response times), with the value of 1
standing for the moment when a response was given. Although
downward- and upward-moving targets do not elicit different
oculomotor behaviors during stimuli presentation, a clear diver-
gence can be seen during response, when the participant’s gaze
tends to drift downward while she or he is adjusting the cursor to
indicate the remembered vanishing location for ascending targets.
It thus seems that a larger number and amplitude of corrective eye
movements are made when indicating the remembered vanishing
location of upward-moving targets as compared with downward
motions.
As for the behavioral results, only a main effect of motion
direction was found in M-displacement, with descending targets
resulting in a significant higher mislocalization in the direction of
motion than ascending ones, F(1, 9) ⫽20.83, p⫽.001, partial
␩
2
⫽.7; linear contrast: F(1, 9) ⫽20.83, p⫽.001, partial ␩
2
⫽
.7. The interaction between target size and motion direction was
found to be nonsignificant, F(2, 18) ⬍1. In O-displacement, both
target size, F(2, 18) ⫽3.9, p⫽.038, partial ␩
2
⫽.3; linear
contrast: F(1, 9) ⫽7.26, p⫽.025, partial ␩
2
⫽.45, and motion
direction, F(1, 9) ⫽7.7, p⫽.022, partial ␩
2
⫽.46; linear contrast:
F(1, 9) ⫽7.71, p⫽.022, partial ␩
2
⫽.46, were significant. The
interaction between target size and motion direction was only
marginally significant, F(2, 18) ⫽3.27, p⫽.062, partial ␩
2
⫽.26;
with a significant bilinear contrast, F(1, 9) ⫽7.78, p⫽.021,
partial ␩
2
⫽.46. The remembered vanishing location for bigger
targets was displaced leftward, toward the fixation dot, and slightly
more so for descending targets. No other main effects or interac-
tions reached statistical significance. Panels A and C of Figure 7
show the mean M- and O-displacement, respectively, for the
ascending targets (white markers and dashed lines) and descending
targets (black targets and continuous lines) in the SP task.
Constrained eye movement task. As in the CM task in
Experiment 1, trials where participants’ gaze moved outside a
region of interest of 30 px around the fixation dot were excluded
(1.6% of the total number of trials). Overall, in contrast with the SP
task, M-displacement was negative, thus signaling a mnesic dis-
placement against the target’s motion, toward the fixation dot and,
Figure 6. Mean vertical gaze positions for downward (full lines) and upward (dashed lines) moving targets as
a function of time (abscissa) in Experiment 3 (SP task). Panel A depicts the gaze positions from .5 s before to
.5 s after target’s disappearance. The dotted line depicts the trajectory of the target. Panel B depicts the gaze
positions as a function of normalized response times, such that 1 stands for the moment a response was given.
Notice that the ordinate represents gaze position in reference to target’s motion, so that negative numbers refer
to gaze locations behind the vanishing location of the target (smooth pursuit) and positive numbers to locations
beyond (overshoot). SP ⫽smooth pursuit; px ⫽pixels.
Figure 7. M- (panels A and B) and O-displacements (panels C and D) as
a function of size (abscissas) for downward (black circles and full lines)
and upward (white circles and dashed lines) moving targets. The left
column (panels A and C) refers to the SP task and the right column (panels
B and D) refers to the CM task, in Experiment 3. Error bars indicate
standard errors of the mean. SP ⫽smooth pursuit; CM⫽constrained eye
movements; M-displacement ⫽mislocalization along the target’s trajec-
tory (M ⫽motion axis); O-displacement ⫽errors along the axis orthog-
onal to the target’s trajectory (O ⫽orthogonal axis); px ⫽pixels.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1673
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

therefore, gaze location. Target size, F(2, 18) ⫽7.54, p⫽.004,
partial ␩
2
⫽.45; linear contrast: F(1, 9) ⫽20.47, p⫽.001, partial
␩
2
⫽.69; onscreen vanishing location, F(2, 18) ⫽93.59, p⬍.001,
partial ␩
2
⫽.91; linear contrast: F(1, 9) ⫽168.48, p⬍.001, partial
␩
2
⫽.95; and motion direction, F(1, 9) ⫽6.53, p⫽.031, partial ␩
2
⫽
.42; linear contrast: F(1, 9) ⫽6.53, p⫽.031, partial ␩
2
⫽.42, were
all shown to significantly modulate M-displacement’s magnitude. It
is important to highlight that the effect of target size was not
modulated by the direction of motion, as signaled by a null
interaction, F(2, 18) ⬍1.
Descending targets led to a less negative M-displacement than
did ascending ones (see Figure 7, panel B). Vanishing positions
further apart from the fixation dot resulted in increasingly negative
M-displacements (70-px condition: M⫽⫺11.53, SD ⫽15.8;
90-px condition: M⫽⫺20.3, SD ⫽19.2; 110-px condition:
M⫽⫺33.13, SD ⫽16.3). Finally, bigger targets resulted in less
M-displacement than did smaller ones (see Figure 7, panel B); that
is, the remembered vanishing location for bigger targets was more
displaced toward gaze than smaller ones. A similar pattern was
found for O-displacement (see Figure 7, panel D), with bigger
targets significantly more displaced leftward than smaller ones,
F(2, 18) ⫽10.65, p⫽.001, partial ␩
2
⫽.54; linear contrast: F(1,
9) ⫽14.5, p⫽.004, partial ␩
2
⫽.62. Taken together, these
outcomes further strengthen our previous finding that the memory
for the position of bigger targets is more drawn to the gaze location
(foveal bias) than is that for smaller targets.
Discussion of Experiment 3
The outcomes once again disclosed a significant effect of target
size on foveal bias, with bigger targets remembered as further
displaced toward the fixation dot when no eye movements were
allowed. The hypothesis that an effect of perceived target’s heavi-
ness emerges only when the motion is aligned with the gravity pull
(thus reflecting an intuitive notion of the physical behavior of
heavier targets) does not seem to hold in light of the found
patterns. In fact, as regards to target sizes, the found outcomes
closely mimic the results of Experiment 1. Motion direction seems
thus to be unrelated with the effect of target size on the behavioral
localizations disproving an account based on perceived heaviness.
Of importance, when no constraints are imposed on eye move-
ments, even though no effect in M-displacement emerges, bigger
targets result in a bigger O-displacement leftward, toward the
fixation dot. Although for horizontally moving targets (Experiment
1) the latter corresponded to mislocalizations in the direction of
gravity, for vertically moving targets they are orthogonal to that
direction. Although in the CM tasks a foveal bias proportional with
target size is evident, the outcomes disclosed in the SP tasks
suggest that the mere presence of a fixation point might, as in
Experiment 1, engage other mechanisms in the modulation of the
spatial judgments (see Sheth & Shimojo, 2001, for a related
observation). When no eye movement constraints are imposed, the
presence and location of a fixation dot seem to be the explaining
factors, not gravity or the target’s perceived weight.
We found a significantly bigger displacement in the direction of
motion for descending as opposed to ascending targets, irrespec-
tive of the presence or absence of eye movements. This is evidence
that gravity might be playing a role in these spatial localization
tasks. In fact, when eye movements are allowed, the smooth
pursuit and an ocular overshoot are equally evident for downward-
and upward-moving targets with no apparent differences. Only
when participants are providing their responses (i.e., while they are
adjusting the cursor in the desired position) does a divergence in
the gaze location emerge between ascending and descending tar-
gets. This result is similar to that found in oculomotor behavior for
horizontally moving targets in Experiment 1 (SP task). It is im-
portant to note that the found pattern of eye movements during
response seems to be driven internally, as the target is no longer
present. In this sense, the corrective eye movements found while
adjusting the cursor seem to result from a representational or
mnesic process. We thus surmise that both eye movements and the
behavior localization responses are sensitive to an internal model
of gravity (see also De Sá Teixeira, Hecht, & Oliveira, 2013).
Experiment 4: Representational Trajectory for
Vertically Moving Targets With Varying Sizes
In the previous experiment, we found evidence that vertically
moving, bigger targets, instead of being perceived as heavier and
thus mislocalized downward, are displaced toward gaze when eye
movements are not allowed. This outcome adds to the findings
reported in Experiment 1. When no eye constraints were imposed,
M-displacement was found to be unaffected by target size. This
result is in contrast with the finding reported by Hubbard (1997),
where bigger targets were found to interact with the direction of
motion such that the remembered vanishing location of descending
targets was increased forward for bigger targets, as compared with
ascending motions. Given the results we reported so far in the
present paper, we can hypothesize that the presence of the fixation
point in our experiment, absent in the tasks conducted by Hubbard,
might be responsible for the discrepancy. The mere presence of a
fixation dot, which has been reported to result in a spatial bias
(Sheth & Shimojo, 2001), might have masked a possible effect of
target size in our task. Furthermore, it might also be the case that
with increasing temporal intervals between the target’s offset and
initiation of the response, the remembered vanishing location for
bigger ascending and descending targets evolves differently. Such
a trend might support an effect of the perceived object’s heaviness
on representational momentum if bigger targets are found to lead
to increasingly bigger displacements downward with longer inter-
vals.
The next experiment aims to explore these possibilities by (a)
presenting vertically moving targets with no other spatial visual
cues (e.g., fixation point) and (b) imposing retention intervals
between participant responses and the disappearance of the targets.
On the basis of previous unpublished experiments that suggested
that representational trajectory for vertically moving targets pos-
sesses a longer time course, we used retention intervals ranging
from 0 to 1,200 ms. We predicted that, in accordance with Hub-
bard’s results, with no fixation point bigger targets would lead to
increased displacements downward (in the direction of motion for
descending targets but opposed to the direction of motion for
ascending targets). Also, if perceived heaviness does modulates
the forward displacement of vertically moving targets, we ex-
pected to find that with increasing temporal intervals between the
target’s offset and the initiation of the response, a difference
between the remembered vanishing locations for bigger ascending
and descending targets would emerge.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1674 DE SÁ TEIXEIRA AND OLIVEIRA

Method
Participants. Twenty new participants (4 male, 16 female)
were recruited for the experiment. Their ages ranged from 18 to 21
years (M⫽18.9, SD ⫽.97), and all of them had normal or
corrected to normal vision.
Stimuli. Animations in all respects alike the ones employed in
the previous experiment were used as stimuli. All targets were
shown moving vertically (upward or downward) at a constant
velocity of 300 px/s, and they vanished after covering 70 or 110
pixels beyond the center of the screen. No fixation point was
shown. Retention intervals of 0, 300, 600, 900, or 1,200 ms were
imposed after the vanishing of the target and before the appearance
of the plus-shaped cursor.
Procedure and design. The procedure was in all respects
alike the one used in the SP task in Experiment 3, with the
exception that no eye movements were recorded. Also, no con-
straints in head movements were imposed, although participants
were instructed to maintain a steady posture during the entire
experiment with their cyclopean eye at about 50 cm from the
center of the screen. The experiment followed a 3 (target size) ⫻
2 (vanishing position) ⫻2 (motion direction) ⫻5 (retention
interval) repeated measures design with three repetitions. Each
participant completed 180 trials, and the entire experiment, includ-
ing instructions and debriefing, lasted for about 40 minutes.
Results
M- and O-displacements were calculated as in the previous
experiment. Figure 8 shows the obtained M-displacements as a
function of retention interval (abscissa) for the downward (panel
A) and upward (panel B) movements and the different target sizes
(line parameters). It can be seen that, overall, bigger targets led to
bigger M-displacements, F(2, 38) ⫽13.69, p⬍.001, partial ␩
2
⫽
.42; linear contrast: F(1, 19) ⫽26.67, p⬍.001, partial ␩
2
⫽.58,
for both directions. However, the effect of target size increased
(vertical spread of lines in Figure 8) more for the 0-ms retention
interval than for longer times with descending targets, while for
ascending ones the effect of target size was roughly constant
across the entire range of times. These trends were evidenced in a
significant three-way statistical interaction among target size, di-
rection, and retention time, F(8, 152) ⫽3.1, p⫽.003, partial ␩
2
⫽
.14; with a significant linear-linear-quadratic contrast, F(1, 19) ⫽
15.3, p⫽.001, partial ␩
2
⫽.45. Finally, the onscreen vanishing
location once again was shown to modulate the magnitude of
M-displacement, F(1, 19) ⫽18.43, p⬍.001, partial ␩
2
⫽.49;
linear contrast: F(1, 19) ⫽18.43, p⬍.001, partial ␩
2
⫽.49 (70-px
condition: M⫽22.24, SD ⫽21.42; 110-px condition: M⫽13.3,
SD ⫽21). No other main effects or interactions were significant in
M- or O-displacement.
Discussion of Experiment 4
The outcomes of Experiment 4 do not seem to support an effect
of target size as a proxy for the perceived object’s heaviness, as
bigger targets did not reveal a different downward drift. Instead,
we found approximately similar effects of target size for ascending
and descending targets, with the sole exception of the 0-ms con-
dition with downward-moving targets, which replicated the con-
ditions of the experiment reported by Hubbard (1997).
Overall, bigger targets resulted in a higher displacement in the
direction of motion for both ascending and descending targets.
This effect was significantly increased with downward-moving
objects but only for the 0-ms condition. That this trend is absent
with longer retention intervals casts doubts on an interpretation in
terms of a cognitive analogue of heaviness.
In sum, we found no evidence for an effect of perceived target’s
heaviness in either representational momentum or representational
gravity. Target size seems to determine instead the degree of
foveal bias in the remembered vanishing locations. Particular
patterns of oculomotor behavior, by determining gaze location and
therefore foveal bias, seem thus to be responsible for previously
reported effects of implied mass.
General Discussion
Previous studies have reported that varying the sizes of moving
targets affects the spatial memory of the vanishing location, with
bigger targets leading to increased errors forward in the direction
of motion (representational momentum; De Sá Teixeira, de Ol-
iveira, & Amorim, 2010;De Sá Teixeira, Oliveira, & Simões,
Figure 8. Mean M-displacements found in Experiment 4 as a function of temporal intervals (abscissa) and
target size (line parameters) for the downward (panel A, full lines) and upward (panel B, dashed lines) moving
targets. Error bars indicate standard errors of the mean. M-displacement ⫽mislocalization along the target’s
trajectory (M ⫽motion axis); px ⫽pixels.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1675
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

2010;De Sá Teixeira, Pimenta, & Raposo, 2013) and downward in
the direction of gravity (representational gravity; Hubbard, 1995,
1997). These outcomes were interpreted as reflecting an effect of
perceived target’s mass and/or heaviness. Our main purpose was to
investigate the effects of target size on spatial memory and to
provide support for the account that those errors reflect internal-
ized notions of the physical behavior of heavier objects. Contrary
to our initial prediction, no evidence was found to support the
hypothesis that representational momentum is sensitive to per-
ceived mass. Also, contrary to the claim made by Hubbard (1997),
we found no evidence that the target’s perceived heaviness mod-
ulates representational gravity. Instead, we disclosed a systematic
and reliable proneness of participants to remember the vanishing
locations as more displaced toward their gaze for bigger targets, at
least when eye movements were constrained or when no other
visual element besides the target (e.g., fixation dot) was present
onscreen. The uncovered effects, rather than being compatible
with the hypothesis of an internalization of momentum, seem
instead to reflect spatial biases in behavioral localizations. Said
another way, our outcomes seem to be better accounted for by
foveal and spatial biases than by cognitive analogues of physical
properties.
Thus, in Experiments 1 and 3 bigger targets were more dis-
placed toward gaze location when participants’ eye movements
were constrained. On the other hand, in Experiments 2a and 4, with
neither eye movements’ constraints nor the presence of a fixation
dot, bigger targets were shown to be mislocalized by a greater
amount forward in the direction of the target’s motion. Based on
the eye-tracking evidence found in Experiments 1 and 3 in the SP
conditions, participants’ eyes tend to overshoot the vanishing
position of a moving target that suddenly disappeared; thus, the
effect of target size can be taken to reflect likewise a bigger foveal
bias for bigger targets. This picture is altered when (a) there is a
fixation dot present onscreen (Experiments 1 and 3, SP conditions)
and (b) when the target moves at slower speeds (Experiment 2b).
The latter can be accounted for by the fact that the magnitude of
ocular overshoot depends on the target velocity: Slower targets
result in a smaller ocular overshoot, and the effect of target size on
foveal bias is therefore reduced (notice, however, that our data
suggest that this might depend on the context of observed kine-
matics). The former implies that a visual spatial reference (fixation
dot) competes with gaze in the modulation of target size. These
outcomes are summarized in Figure 9, where the locations on-
screen are plotted for the different sizes and vanishing locations
when eye movements are constrained (Panel A; CM tasks in
Experiments 1 and 3; only the 300-px/s velocity conditions are
plotted), when participants are free to move their eyes with the
presence of a fixation dot (Panel B; SP tasks in Experiments 1 and
3; only the 300-px/s velocity is considered) and when the partic-
ipants are free to track the target with their gaze in the absence of
other visual elements (Panel C; Experiments 2a and 4; only the
300-px/s velocity conditions and the 0-ms retention intervals are
plotted).
That the mere presence of a fixation dot affects spatial local-
ization judgments has been previously reported (Sheth & Shimojo,
2001). It is possible that in our tasks the presence and location of
this visual reference have triggered attentional phenomena, known
to modulate foveal bias (Bocianski et al., 2010;Fortenbaugh &
Robertson, 2011). This would explain why no effect of target size
Figure 9. Onscreen bidimensional remembered locations of moving tar-
gets as a function of motion direction, vanishing location, and target size.
Panel A: Remembered vanishing locations when no eye movements are
allowed. The eye pictograms represent gaze location for the horizontal and
vertical motion directions. Data are from Experiments 1 and 3, CM
conditions. Only the 300-px/s velocity conditions are shown. Panel B:
Remembered vanishing locations with free viewing when a fixation dot is
present (plus-shaped markers). Data are from the SP conditions of Exper-
iments 1 and 3. Only the 300-px/s conditions are plotted. Panel C: Re-
membered vanishing locations with smooth pursuit eye movements with no
fixation point present onscreen. Data are from the 0-ms and 300-px/s
conditions of Experiments 2a and 4. SP ⫽smooth pursuit; CM⫽con-
strained eye movements; px ⫽pixels.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1676 DE SÁ TEIXEIRA AND OLIVEIRA

emerges when a fixation dot is present behind the target’s vanish-
ing location (SP condition in Experiments 1 and 3), in contrast
with the outcomes found when no fixation dot is shown (Experi-
ments 2a and 4). If such is the case, we predict that an increased
effect of target size would emerge if a visual cue is presented
ahead of the vanishing position.
It remains to be determined why bigger targets are further
subjected to foveal biases. It might be the case that bigger targets,
by stimulating a wider retinal area, lead to increased uncertainty in
the spatial location of its center and, thus, to observers relying
more on extra-retinal cues, such as gaze location (which might be
accounted for by, e.g., a Bayesian framework). Depending on the
patterns of oculomotor behavior (eye movements constrained or
smooth pursuit ocular overshoot), the memory for the location of
bigger targets would thus be drawn toward the location of gaze
when the object vanished. One other possibility is that bigger
targets, due to the fact that their edges are further apart, stimulate
retinal areas closer to the fovea. This last hypothesis could be
accounted for by the dynamic neural field model proposed by
Jancke et al. (1999; see also Bocianski, Müsseler, & Erlhagen,
2008,2010;Erlhagen, 2003;Erlhahen & Jancke, 2004). The model
assumes that the spatial location of stimuli is encoded by a local
pattern of activity in large populations of excitatory and inhibitory
neurons, each tuned to a specific spatial location. The perceived
spatial locations would depend both on the retinal inputs and the
inherent organization of the neural network. Of importance for the
present purposes, it has been suggested that the weight profiles for
the excitatory and inhibitory neural populations are not symmetric
but rather are slightly shifted toward the fovea (asymmetric weight
profile; cf. Bocianski et al., 2008). That is, each neuron in the
network receives higher inputs from neurons tuned to spatial
locations closer to the fovea. Some empirical evidence has been
gathered that favors this hypothesis (e.g., Jancke & Erlhagen,
2010;Jancke, Erlhagen, Schöner, & Dinse, 2004), and it has been
proposed as the neural substrate for the foveal bias. In our stimuli,
the inner edge of bigger targets would stimulate neurons with
receptive fields closer to the fovea, which, due to the asymmetric
weight profile, would encode the targets’ spatial location as more
displaced toward gaze.
These considerations should be tested in future studies that
present static targets to observers. Because, by definition, repre-
sentational momentum refers to spatial mislocalizations of moving
targets, we did not assess the effects of target size on the spatial
memory with static targets. However, in light of the obtained
outcomes, it is now clear that this avenue of inquiry is certainly
warranted. For instance, the dynamic neural field model entails the
prediction that if participants are asked to locate the inner edge,
instead of the center, of static targets varying in sizes, the magni-
tude of foveal bias would depend solely on the location of that
edge, irrespective of the size of the target. If, on the other hand, the
size of targets modulates foveal bias even when the edges coincide,
an explanation in terms of input uncertainty, as proposed above,
would be favored instead.
Conclusion
We showed that target size, when presented in isolation (i.e.,
with no other visual reference) affects the magnitude of foveal bias
in representational momentum tasks. This outcome came unex-
pectedly, as we hypothesized that bigger targets would be per-
ceived as heavier and thus further displaced forward and down-
ward in memory, irrespective of oculomotor factors. The research
presented here might thus be taken as a cautionary tale regarding
the possible role of extraneous phenomena on spatial localization
tasks, as previously argued by Kerzel (e.g., 2006). Foveal bias,
whether seen as a perceptual, mnesic, or attentional phenomenon
(Bocianski et al., 2010;Fortenbaugh & Robertson, 2011;Sheth &
Shimojo, 2001), does seem to determine, under certain circum-
stances, results previously reported as evidence for an internaliza-
tion or second-order isomorphism of ecologically relevant envi-
ronmental invariants. We do surmise that some spatial localization
phenomena might reflect internalized properties of the natural
environment. In fact, we reported here some results that add to
previous research in supporting a role of an internal model of
gravity in this type of tasks (e.g., De Sá Teixeira, Hecht, &
Oliveira, 2013). Also, we cannot entirely rule out that perceived
mass or heaviness does not influence representational momentum
or representational gravity, but simply that such manipulation
cannot be achieved by variations of target size. Delimiting the
phenomena accounted for by oculomotor, perceptual, mnesic,
and/or attentional phenomena and describing their effects are par-
amount for recognizing, identifying, and understanding which
variables bear a significant role in disclosing the mechanics of
visual representations and which environmental invariants are in-
ternally modeled by an observer. Gravity, for example, seems to be
one such invariant. Perceived mass or heaviness, as manipulated
by variations of target size, does not.
On the plus side, the uncovered outcomes strengthened the
prospect of taking the mouse-pointing task as a correlate of eye
movements. For instance, in De Sá Teixeira, Pimenta, and Raposo
(2013) we found that target size but not target velocity modulated
the spatial localization errors made by patients with schizophrenia.
The ensuing hypothesis was that the null effect of velocity re-
vealed, with a purely psychophysical task, the known deficits in
SPEM previously reported for this population (Chen, 2011), which
tend to track a smoothly moving target with a sequence of saccades
in a sawtooth pattern. Based on the present findings, it might be
hypothesized that the patients with schizophrenia in that study
were prone to making a saccadic overshoot forward when tracking
a moving object that disappeared. An effect of target size would
thus emerge, as it did, due to a foveal bias. This possibility holds
the prospect of using the present paradigm to easily assess some
aspects of oculomotor function. A similar case could be made for
future studies on representational momentum: Given a fixation
instruction and in the impossibility, for whatever reason, of mea-
suring eye movements, a null effect of target velocity could be
taken as evidence that participants complied with the instruction;
that is, the effect of target velocity can be reliably used as a
manipulation check when preventing SPEM, at least for displays
similar to the ones used in the present experiments. Likewise, the
effect of target size, with no other competing reference, can be
taken as a correlate of foveal bias, whenever a researcher suspects
that that might be an important factor to consider. However,
further studies should be conducted in order to firmly establish a
link between behavioral localization responses and eye-tracking
patterns.
As a final observation, we showed in the present paper how the
temporal profile of spatial localizations (representational trajec-
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1677
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS

tory; Experiments 2a, 2b, and 4) could be instrumental in testing
hypotheses regarding representational gravity. The finding that
target size does not modulate the rate at which the spatial memory
drifts downward further disproves that perceived heaviness is an
explaining factor to consider in these displays.
References
Bertamini, M. (1993). Memory for position and dynamic representations.
Memory & Cognition, 21, 449–457. doi:10.3758/BF03197176
Bocianski, D., Müsseler, J., & Erlhagen, W. (2008). Relative mislocaliza-
tion of successively presented stimuli. Vision Research, 48, 2204–2212.
doi:10.1016/j.visres.2008.06.016
Bocianski, D., Müsseler, J., & Erlhagen, W. (2010). Effects of attention on
a relative mislocalization with successively presented stimuli. Vision
Research, 50, 1793–1802. doi:10.1016/j.visres.2010.05.036
Chen, Y. (2011). Abnormal visual motion processing in schizophrenia: A
review of research progress. Schizophrenia Bulletin, 37, 709–715. doi:
10.1093/schbul/sbr020
Collewijn, H., & Tamminga, E. P. (1984). Human smooth and saccadic eye
movements during voluntary pursuit of different target motions on
different backgrounds. Journal of Physiology, 351, 217–250.
Cooper, L. A., & Munger, M. P. (1993). Extrapolations and remembering
positions along cognitive trajectories: Uses and limitations of analogies
to physical momentum. In N. Eilen, R. McCarthy, & B. Brewer (Eds.),
Spatial representation: Problems in philosophy and psychology (pp.
11–131). Cambridge, MA: Blackwell.
De Sá Teixeira, N. A., de Oliveira, A. M., & Amorim, M.-A. (2010).
Combined effects of mass and velocity on forward displacement and
phenomenological ratings: A functional measurement approach to the
momentum metaphor. Psicologica, 31, 659–676.
De Sá Teixeira, N. A., Hecht, H., & Oliveira, A. M. (2013). The repre-
sentational dynamics of remembered projectile locations. Journal of
Experimental Psychology: Human Perception and Performance, 39,
1690–1699. doi:10.1037/a0031777
De Sá Teixeira, N. A., & Oliveira, A. M. (2011). Disambiguating the
effects of target travelled distance and target vanishing point upon
representational momentum. Journal of Cognitive Psychology, 23, 650–
658. doi:10.1080/20445911.2011.557357
De Sá Teixeira, N. A., Oliveira, A. M., & Simões, F. (2010). Modelização
dos efeitos da massa e da velocidade do alvo na magnitude do momento
representacional [Modeling the effects of mass and velocity of the target
in the magnitude of representational momentum]. Psicologia & Educa-
ção, 1(2), 31–40.
De Sá Teixeira, N., Pimenta, S., & Raposo, V. (2013). A null effect of
target’s velocity in the visual representation of motion with schizo-
phrenic patients. Journal of Abnormal Psychology, 122, 223–230. doi:
10.1037/a0029884
Erlhagen, W. (2003). Internal models for visual perception. Biological
Cybernetics, 88, 409–417. doi:10.1007/s00422-002-0387-1
Erlhagen, W., & Jancke, D. (2004). The role of action plans and cognitive
factors in motion extrapolation: A modelling study. Visual Cognition,
11, 315–341. doi:10.1080/13506280344000293
Fortenbaugh, F. C., & Robertson, L. C. (2011). When here becomes there:
Attentional distribution modulates foveal bias in peripheral localization.
Attention, Perception, & Psychophysics, 73, 809–828. doi:10.3758/
s13414-010-0075-5
Freyd, J. J. (1983). The mental representation of movement when static
stimuli are viewed. Perception & Psychophysics, 33, 575–581. doi:
10.3758/BF03202940
Freyd, J. J., & Finke, R. A. (1984). Representational momentum. Journal
of Experimental Psychology: Learning, Memory, and Cognition, 10,
126–132. doi:10.1037/0278-7393.10.1.126
Freyd, J. J., & Finke, R. A. (1985). A velocity effect for representational
momentum. Bulletin of the Psychonomic Society, 23, 443–446. doi:
10.3758/BF03329847
Freyd, J. J., & Johnson, J. Q. (1987). Probing the time course of represen-
tational momentum. Journal of Experimental Psychology: Learning,
Memory, and Cognition, 13, 259–268. doi:10.1037/0278-7393.13.2.259
Freyd, J. J., Kelly, M. H., & DeKay, M. L. (1990). Representational
momentum in memory for pitch. Journal of Experimental Psychology:
Learning, Memory, and Cognition, 16, 1107–1117. doi:10.1037/0278-
7393.16.6.1107
Hubbard, T. L. (1995). Cognitive representation of motion: Evidence for
friction and gravity analogues. Journal of Experimental Psychology:
Learning, Memory, and Cognition, 21, 241–254. doi:10.1037/0278-7393
.21.1.241
Hubbard, T. L. (1996). Representational momentum, centripetal force, and
curvilinear impetus. Journal of Experimental Psychology: Learning,
Memory, and Cognition, 22, 1049–1060. doi:10.1037/0278-7393.22.4
.1049
Hubbard, T. L. (1997). Target size and displacement along the axis of
implied gravitational attraction: Effects of implied weight and evidence
of representational gravity. Journal of Experimental Psychology: Learn-
ing, Memory, and Cognition, 23, 1484–1493. doi:10.1037/0278-7393
.23.6.1484
Hubbard, T. L. (1998). Some effects of representational friction, target
size, and memory averaging on memory for vertically moving targets.
Canadian Journal of Experimental Psychology, 52, 44–49. doi:10.1037/
h0087278
Hubbard, T. L. (2005). Representational momentum and related displace-
ments in spatial memory: A review of the findings. Psychonomic Bul-
letin & Review, 12, 822–851. doi:10.3758/BF03196775
Hubbard, T. L. (2006). Computational theory and cognition in representa-
tional momentum and related types of displacement: A reply to Kerzel.
Psychonomic Bulletin & Review, 13, 174–177. doi:10.3758/
BF03193830
Hubbard, T. L., & Bharucha, J. J. (1988). Judged displacement in apparent
vertical and horizontal motion. Perception & Psychophysics, 44, 211–
221. doi:10.3758/BF03206290
Hubbard, T. L., Blessum, J. A., & Ruppel, S. E. (2001). Representational
momentum and Michotte’s (1946/1963) “launching effect” paradigm.
Journal of Experimental Psychology: Learning, Memory, and Cogni-
tion, 27, 294–301. doi:10.1037/0278-7393.27.1.294
Hubbard, T. L., & Ruppel, S. E. (2002). A possible role of naive impetus
in Michotte’s “Launching Effect”: Evidence from representational mo-
mentum. Visual Cognition, 9, 153–176. doi:10.1080/1350628014300
0377
Jancke, D., & Erlhagen, W. (2010). Bridging the gap: A model of common
neural mechanisms underlying the Fröhlich effect, the flash-lag effect,
and the representational momentum effect. In R. Nijhawan & B.
Khurana (Eds.), Space and time in perception and action (pp. 422–440).
New York, NY: Cambridge University Press.
Jancke, D., Erlhagen, W., Dinse, H., Akhavan, A., Giese, M., Steinhage,
A., & Schöner, G. (1999). Parametric population representation of
retinal location: Neuronal interaction dynamics in cat primary visual
cortex. Journal of Neuroscience, 19, 9016–9028.
Jancke, D., Erlhagen, W., Schöner, G., & Dinse, H. (2004). Shorter
latencies for motion trajectories than for flashes in population responses
of cat primary visual cortex. Journal of Physiology, 556, 971–982.
doi:10.1113/jphysiol.2003.058941
Kerzel, D. (2000). Eye movements and visible persistence explain the
mislocalization of the final position of a moving target. Vision Research,
40, 3703–3715. doi:10.1016/S0042-6989(00)00226-1
Kerzel, D. (2002). The locus of “memory displacement” is at least partially
perceptual: Effects of velocity, expectation, friction, memory averaging,
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1678 DE SÁ TEIXEIRA AND OLIVEIRA

and weight. Perception & Psychophysics, 64, 680–692. doi:10.3758/
BF03194735
Kerzel, D. (2003). Centripetal force draws the eyes, not memory of the
target, toward the center. Journal of Experimental Psychology: Learn-
ing, Memory, and Cognition, 29, 458–466. doi:10.1037/0278-7393.29
.3.458
Kerzel, D. (2006). Why eye movements and perceptual factors have to be
controlled in studies on “representational momentum” Psychological
Bulletin & Review, 13, 166–173. doi:10.3758/BF03193829
Kerzel, D., Jordan, J. S., & Müsseler, J. (2001). The role of perception in
the mislocalization of the final position of a moving target. Journal of
Experimental Psychology: Human Perception and Performance, 27,
829–840. doi:10.1037/0096-1523.27.4.829
Krauzlis, R. J., & Stone, L. S. (1999). Tracking with the mind’s eye. Trends
in Neurosciences, 22, 544–550. doi:10.1016/S0166-2236(99)01464-2
Land, M., & Tatler, B. (2009). Looking and acting. Oxford, United King-
dom: Oxford University Press.
Michotte, A. (1954). La perception de la causalité [Perception of causa-
tion] (2nd éd.). Louvain, France: Études de Psychologie.
Mitrani, L., & Dimitrov, G. (1978). Pursuit eye movements of a disap-
pearing moving target. Vision Research, 18, 537–539. doi:10.1016/
0042-6989(78)90199-2
Müsseler, J., van der Heijden, A. H. C., Mahmud, S. H., Deubel, H., &
Ertsey, S. (1999). Relative mislocalization of briefly presented stimuli in
the retinal periphery. Perception & Psychophysics, 61, 1646–1661.
doi:10.3758/BF03213124
Nagai, M., Kazai, K., & Yagi, A. (2002). Larger forward memory dis-
placement in the direction of gravity. Visual Cognition, 9, 28–40.
doi:10.1080/13506280143000304
Shepard, R. N. (1984). Ecological constraints on internal representation:
Resonant kinematics of perceiving, imagining, thinking, and dreaming.
Psychological Review, 91, 417–447. doi:10.1037/0033-295X.91.4.417
Shepard, R. N., & Chipman, S. (1970). Second-order isomorphism of
internal representations: Shapes of states. Cognitive Psychology, 1,
1–17. doi:10.1016/0010-0285(70)90002-2
Shepard, R. N., & Metzler, J. (1971, February 19). Mental rotation of
three-dimensional objects. Science, 171, 701–703. doi:10.1126/science
.171.3972.701
Sheth, B. R., & Shimojo, S. (2001). Compression of space in visual
memory. Vision Research, 41, 329–341. doi:10.1016/S0042-
6989(00)00230-3
Received September 30, 2013
Revision received February 10, 2014
Accepted February 16, 2014 䡲
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1679
BIASES, TARGET SIZE, AND SPATIAL MISLOCALIZATIONS