Intelligent Information Management, 2010, 2, 90-94
doi:10.4236/iim.2010.22011 Published Online February 2010 (
Copyright © 2010 SciRes IIM
Distortion of Space and Time during Saccadic
Eye Movements
Masataka Suzuki1, Yoshihiko Yamazaki2
1 Department of Psychology, Kinjo Gakuin University, Nagoya, Japan
2 Department of Computer Science and Engineering Graduate School of Engineering
Nagoya Institute of Technology, Nagoya, Japan
The space-time distortion perceived subjectively during saccadic eye movements is an associative phe-
nomenon of a transient shift of observer’s visual frame of reference from one position to another. Here we
report that the lines of subjective simultaneity defined as two spatially separated flashes perceived during
saccades were nearly uniformly tilted along the physical time-course. The causality of the resulting
space-time compression may be explained by the Minkowski space-time diagram in physics.
Keywords: Saccade Space Time Compression
1. Introduction
In vision, an observer’s frame of reference is one of the
necessary elements of perceiving an event in space
(where) and time (when). During saccadic eye move-
ments, a space once recognized in one frame of reference
is distorted toward the target as the eye fixates it in the
new frame of reference [1,2]. Morrone et al. [3] demon-
strated that the resulting space compression accompanies
an underestimation of the perceived time interval be-
tween temporally separated stimuli. Since these two il-
lusory effects occurred in nearly the same time range,
they suggested the possibility of a single unifying
mechanism of both the space and time compressions.
Moreover, they speculated that the space-time compres-
sion is originated from anticipatory repositioning of visual
receptive fields [4–6], leading to an immediate relativis-
tic consequence in perceptual space and time [7]. To ap-
proach this mechanism, however, it is necessary to probe
into the transient dynamics of these illusions [8]. In this
study, we provide psychophysical evidence that the
space-time compression during saccadic eye movements
could be attributable to the backward temporal shift of
time-course by which the observer perceives the saccade
target in a new frame of reference. These effects on visual
percepts of space, time and simultaneity may be ex-
plained along the framework of a ‘thought experiment’ of
special relativity theory [9].
2. Methods
In this study, observers made a judgment as to the simultaneity
of two briefly flashed stimuli appearing at different times
during the course of a horizontal saccade (Figure 1(a)).
The observers were seated in the dark, with their head
fixed by a chin- and forehead-rest. Two-colored LEDs
positioned on the black board in front of the observers
(viewing distance: 40cm), were used as a central fixation
target (FT) and a saccade target (ST) (panel 1 in Figure
1a). After fixating to the fixation target (FT) for a period
of time between 1500 and 2500 ms, both the FT and
saccade targets (ST) were turned off simultaneously
(pane 2 in Figure 1(a)), and the observers made a 30 de-
grees (º) horizontal saccade to the remembered ST as
soon as both targets disappeared. Either of the FT or ST
was also used to provide a standard stimulus (SS) or a
comparison stimulus (CS), respectively. The early rising
phase of electro-oculographic (EOG) signal less than
15% relative to its maximal value was used as a common
triggering source (CTS) of SS and CS, each of which
provides a flash with short exposure time (1 ms) at dif-
ferent latencies from CTS (e.g., see panel 3 in Figure 1(a)).
The short exposure (1 ms) of flashed stimuli effectively
minimized motion blur during saccades, allowing for the
observers to specify the apparent positions of the two
In the first condition (Cond. 1), FT and ST provide SS
and CS, respectively (e.g., see panel 3 in Figure 1(a)),
while in the second condition (Cond. 2) they provide CS
and SS, respectively. The SS was flashed at different
constant latencies of 20, 33, 50 or 100 ms from a CTS
signal. In each latency condition, the experimenter initially
set the time interval of CS and SS far below or far above
the observer’s threshold, and the observers were asked to
adjust the variable timing of the CS on a trial-by-trial
basis until it appeared equal to the latency of the SS, and
to report corresponding spatial positions of the two
flashes (e.g., see panel 4 in Figure 1(a)). In each of these
ascending or descending sessions, the timing of the CS
relative to that of SS was varied by the observer con-
tinuously via a dial on a pulse generator, and apparent
position of two flashes perceived as simultaneous during
the course of the saccade was pointed by the observer on
a trial-by-trial basis, by adjusting the sensor head of a
linear potentiometer (Novotechnik, TLH1000, length 0.8
m), fixed sideways along a black board. In Cond.1 and 2,
the subjective simultaneity of two flashes was estimated
from the mean of five sets of ascending and descending
sessions in each latency condition.
Horizontal eye position was recorded using an EOG
system (AVH-10, Nihon-Koden) by placing Ag-AgCl
skin electrodes at the outer canthi of both eyes. A ground
electrode was placed just above the eyebrows in the cen-
ter of the forehead. As described earlier, the early rising
phase of the EOG signal was used to trigger two pulse
generators for the LED flashes of SS and CS. The base
line adjustment of EOG signal was carried out carefully
on a trial-by-trial basis. Target presentation and data col-
lection were controlled using custom software pro-
grammed in LabVIEW (National Instruments). The eye
position signals were digitally low-passed filtered at 50
Hz, using a second-order Butterworth filter implemented
in MatLab (The Mathworks). The onsets of eye move-
ment were scored on the basis of 5% of the peak velocity
of their position signals. Seven and six observers were
used in Cond. 1 and Cond. 2, respectively.
3. Results
The spatial relationship between the perceived positions
of the SS flashes and the corresponding eye positions
was out-of-phase in both conditions (Figure 1(b), (c)). In
Cond. 1, just after the instant of the saccade the SS ap-
pearing on FT was greatly mislocalized once nearest to
the ST, but appeared near to the initial FT position as the
eye fixated on the ST. In Cond. 2, the SS triggered 20 ms
after the onset of CTS was invisible on ST, but in other
Figure 1. Subjective simultaneity of two flashes. (a) Spatial
layout of two targets (FT, ST) and perceived flash stimuli
specified on a black board. The same two-colored LEDs
were used for both FT and ST targets. 1) FT (red) and ST
(red) presented simultaneously at -30º right and 0º (screen
center), respectively. 2) latency period from the simultane-
ous disappearance of two targets. White circles are not real,
but are to refer the spatial position of the two targets. 3) a
typical example of Cond. 1, showing that the spatial posi-
tion of a FT flash (green) is greatly mislocalized toward the
ST, and the ST flash triggered at the same time with the FT
flash is invisible. 4) spatial positions of ST and FT flashes
perceived as simultaneous. (b) Space-time diagram of two
flashes perceived as simultaneous. The lines of subjective
simultaneity in all latency conditions are represented by the
solid and dashed lines in Cond.1 and Cond. 2, respectively.
In Cond. 1, a pair of black or red diamonds represents the
averaged estimate for the tasks when the latencies of SS
flashes from the CTS signals are set at 0 or 33 ms, respec-
tively. In Cond. 2, similarly, red, blue, green and magenta
circles represent the averaged estimate for the tasks when
latencies of SS flashes from the CTS signals were set at 20,
33, 50 and 100 ms, respectively. Note when SS latency from
the CTS signal was set at 20 ms, the flash on the ST was
invisible and thus the CTS signal (red) is depicted alone. (c)
The corresponding amplitudes of the EOG signal to the
flash times of a pair of SS and CS in panel b. Each value is
normalized to the magnitude at 100 ms after the movement
ends. Small panel on the right (asterisk) shows enlarged
representation of latencies and amplitudes of the CTS for
all tasks. Note that the variations of CTS measures are lim-
ited in time and amplitudes across all tasks. Three vertical
bars in panels b) and c) represent means.d. of eye move-
ment times for all tasks and subjects.
Copyright © 2010 SciRes IIM
tasks it was clearly identified, having a negative rela-
tionship to eye position, similar to the Cond.1.
In both conditions, when two stimuli were presented
simultaneously, the ST flashes were perceived to occur
earlier than the FT flashes across the saccadic period.
Therefore, the observers estimated the simultaneity of
the two flashes by delaying the onset time of the ST flash
relative to that of FT in Cond. 1 (e.g., see panel 4 in Fig
1(a)), or by preceding the onset time of FT flash relative
to the ST in Cond. 2 (Figure 1(b)). In Cond. 1, the time
intervals of two flashes as an estimate of the subjective-
simultaneity averaged 25 (± 2) and 16 (± 1) ms, for SS
set at 0 and 33 ms from the onset of CTS, respectively
(solid lines). In Cond. 2 the ST at less than 30 ms after
saccade onsets was invisible, so the same measures of
subjective simultaneity of the two flashes were limited to
the other three cases, averaging 22 (± 1), 16 (± 4) and 2
(± 1) ms, for SS set at 33, 50 and 100 ms from the onset
of CTS, respectively (dashed lines). In both conditions,
therefore, the subjective simultaneity of two flashes can
be referred to as the rightward tilt of the lines of simul-
taneity and as their directional uniformity across the
saccadic period.
The effect of target eccentricity on perceiving simul-
taneity of two flashes was examined under static condi-
tions without a saccade. The observers gazed -30º, -15º
or 0º relative to the ST, and flash stimuli (SS/CS) were
provided by two targets positioned at -5º/5º, -15º/5º or
-30º/0º, respectively. These spatial relationships between
gaze directions and two flashes were roughly analogous
to those in Cond. 2 (Figure 1 (b), (c)). Both stimuli were
given by the experimenter, while the observers were
asked to synchronize them by adjusting their interval on
a trial-by-trial basis. Two flashes were apparently per-
ceived in all tasks, and their intervals perceived as si-
multaneous averaged 2 (± 2), 1 (± 3) and 2 (± 5) ms at
-30º, -15º and 0º conditions, respectively. In the static
condition, therefore, the effect of target eccentricity on
estimating the subjective simultaneity of two flashes
could be minor.
4. Discussions
In this study, we found that the lines of subjective simul-
taneity defined as two spatially separated flashes during
saccades were nearly uniformly distorted on the physical
time-course (Figure 1(b)). When interpreting this in per-
ceptual space-time, however, two simultaneous events
(flashes) must be on a line parallel to the space axis. This
corresponds to the backward temporal shift of the
time-course of ST flashes, relative to the FT flashes
(Figure 2). When this shift component, herein termed t,
Figure 2. Schematic illustration of the space-time compres-
sion based on our results. Two coordinates, (x, t’) and (x’, t’),
are superimposed, analogues to the Minkowski space-time
diagram. The first is Newtonian space-time coordinates to
define position (x) and time (t’) for a moving object(s) in
real (physical) space-time, and the second is perceptual
space-time coordinates (x’, t’) hypothesized based on the
present experiments. For details, see text.
is applicable over a saccadic period, the invisibility of
the ST flashed during the initial half of the saccadic pe-
riod (Figure 1(b)) could be ascribed to the backward
temporal shift of the flash’s percept beyond the extent of
the conscious time window [10] by the amount t. Simi-
larly, an earlier recovery time of the flash position to the
ST than to the FT near the movement end may be ex-
plained by the same scheme. As for the latter, it is well
established [11] that the target percept at the end of the
saccade is referred backward in time to compensate for
the time lost during saccadic suppression [12,13]. Of
more importance in Figure 2 is the strong dependence of
both the space and time compressions on the backward
shift of the time-course of the ST flashes. This scheme is
different from the convergent type of compression pro-
posed previously [1–3].
Among these, Morrone et al. [3] have shown that time
compression perceived subjectively during saccadic eye
movements is an associative phenomenon of space com-
pression, which was evidenced as a convergent type of
mislocalization of visual stimuli toward the endpoint of
the saccade. They suggested that the resulting alternation
of spatial and temporal metrics of perceptual space-time
would lead to relativistic-like effects on the visual per-
cept [7]. Our results, by contrast, indicate that space and
time compressions could be attributable to the shift
component of mislocalization of visual stimuli. To illus-
trate this, as shown in Figure 2, we define Newtonian
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space-time coordinates (x, t’), where the tilted time axis
t’ is to specify the corresponding position (x) of two
flashes, both moving in the opposite direction to the sac-
cadic eye movement. Since in Newtonian space-time the
geometry of space is Euclidian and the time is universal
for all observers, the simultaneity of two flashes is speci-
fied on the line parallel to the space axis x (e.g., see clock
a and c). However, this was not the case in the perceptual
space-time of our observers. According to the rightward
tilt of the lines of simultaneity over a saccadic period in
figure 1b, the sequence of events from the viewpoint of
our observer may be illustrated graphically by shifting
the timescale on the ST in the diagram backward by an
amount t. This corresponds to a tilt in the space axis
from vertical (x) to leftward (x’: red lines). Note this lead
us to define another space-time coordinates (x’, t’), in
which a hypothetical observer moving with this frame of
reference, sees all events occurring on a line parallel to
the space axis x’ as simultaneous (e.g., see clock b and c).
The superimposed representation of two coordinates, (x,
t’) and (x’, t’), and their interrelationship are analogues to
the Minkowski space-time diagram in special relativity
theory [9]. Thus, considering our results from the view-
point of our observer, three relativistic-like effects, the
lack of absolute simultaneity, space contraction (com-
pression) and time compression, can be expected. First,
the fact that the observers estimated the simultaneity of
two flashes by delaying the time of the ST flash relative
to that of FT by the amount t suggests that during sac-
cadic periods the observers see the two flashes occurring
in the space-time coordinates (x’, t’). As a result, the two
flashes perceived as simultaneous in (x’, t’) are not
simultaneous in (x, t’). Second, if this was the case, as
shown by the distance of two white arrow heads in the
figure, the spatial distances of the two flashes appear to
contract in the direction of motion (space compression).
Third, for this observer, all events happening on the
moving ST flashes are compressed relative to that on the
FT (time compression), or the time passed on the clock c
is dilated relative to time passed on the clock b, by the
amount t. Taken together, what is novel here is to pre-
sent a single unifying mechanism of space and time
compression using the Minkowski diagram [9], in which
the space-time compression during saccades could be
ascribed to the homogeneous distortion of space along a
time scale, rather than the convergent type of compres-
sion proposed by Morrone et al. [3].
5. Conclusions
In the present study, the pattern of space-time distortion
perceived subjectively during saccadic eye movements
was studied in order to gain insights into the nature of
corresponding space-time compression inherent in hu-
man visual perception. We found that the lines of subjec-
tive simultaneity defined as two spatially separated
flashes perceived during saccades were nearly uniformly
tilted along the physical time-course. This tempted us to
speculate that vision may be subject to relativistic effects,
similar to physical relativistic effects that occur at speeds
approaching the speed of light. It is well established that
neuron’s receptive fields or their representation of space
are not static entities but that they start to change peri-
saccadically to bring a visual stimulus defined in pre-
saccadic frame of reference into a post-saccadic frame of
reference [4–6]. When this dynamic coordinate trans-
formation is rapid, approaching the physical limit of
neural information transfer, the relativistic consequences
may be expected.
6. References
[1] M. Lappe, H. Awater and B. Krekelberg, “Postsaccadic
visual references generate presaccadic compression of
space,” Nature 403, pp. 892–895, 2000.
[2] J. Ross, M. C. Morrone, and D. C. Burr, “Compression of
visual space before saccades,” Nature 384, pp. 598–601,
[3] M. C. Morrone, J. Ross, and D. C. Burr, “Saccadic eye
movements cause compression of time as well as space,”
Nature Neuroscience 8, pp. 950–954, 2005.
[4] J. R. Duhamel, C. L. Colby, and M. E. Goldberg, “The
updating of the representation of visual space in parietal
cortex by intended eye movements,” Science 255, pp.
90–92, 1992.
[5] M. Kusunoki and M. E. Goldberg, “The time course of
perisaccadic receptive field shifts in the lateral intrapa-
rietal area of the monkey,” Journal of Neurophysiology
89, pp. 1519–1527, 2003.
[6] M. M. Umeno and M. E. Goldberg, “Spatial processing in
the monkey frontal eye field. I. Predictive visual responses,”
Journal of Neurophysiology 78, pp. 1373–1383, 1997.
[7] M. C. Morrone, J. Ross, and D. C. Burr, “Keeping vision
stable: rapid updating of spatiotopic receptive fields may
cause relativistic-like effects,” In R. Nijhawan (Ed.),
Space and time in perception and action, Cambridge:
Cambridge University Press, 2008.
[8] D. M. Eagleman, “Distortion of time during rapid eye
movements,” Nature Neuroscience 8, pp. 850–851, 2003.
[9] A. Einstein, “Relativity: The Special and General The-
ory,” New York: Henry Holt, 1920.
[10] B. Libet, E. W. J. Wright, B. Feinstein, and D. K. Pearl,
“Subjective referral of the timing for a conscious sensory
experience: a functional role for the somatosensory specific
projection system in man,” Brain 102, pp. 193–224, 1979.
[11] K. Yarrow, P. Haggard, R. Heal, P. Brown, and J. C. Roth-
Copyright © 2010 SciRes IIM
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well, “Illusory perceptions of space and time preserve
cross-saccadic perceptual continuity,” Nature 414, pp.
302–305, 2001.
[12] M. R. Diamond, J. Ross, and M. C. Morrone, “Extrareti-
nal control of saccadic suppression,” Journal of Neuro-
science 20, pp. 3442–3448, 2000.
[13] M. C. Morrone, J. Ross, and D. C. Burr, “Apparent posi-
tion of visual targets during real and simulated saccadic
eye movements,” Journal of Neuroscience 17, pp. 7941–
7953, 1997.