Illusory Perceptions of Space and Time Preserve Cross saccadic Perceptual Continuity

Intelligent Information Management, 2010, 2, 90-94

doi:10.4236/iim.2010.22011 Published Online February 2010 (http://www.scirp.org/journal/iim)

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

Email: msuzuki@kinjo-u.ac.jp

Abstract

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

M. SUZUKI ET AL. 91

observers to specify the apparent positions of the two

flashes.

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 mean s.d. of eye move-

ment times for all tasks and subjects.

Copyright © 2010 SciRes IIM

M. SUZUKI ET AL.

92

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

Copyright © 2010 SciRes IIM

M. SUZUKI ET AL. 93

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.

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