<s>
The	O
tau	B-Application
effect	I-Application
is	O
a	O
spatial	O
perceptual	O
illusion	B-Application
that	O
arises	O
when	O
observers	O
judge	O
the	O
distance	O
between	O
consecutive	O
stimuli	O
in	O
a	O
stimulus	O
sequence	O
.	O
</s>
<s>
Thus	O
,	O
the	O
tau	B-Application
effect	I-Application
reveals	O
that	O
stimulus	O
timing	O
affects	O
the	O
perception	O
of	O
stimulus	O
spacing	O
.	O
</s>
<s>
Time	O
is	O
also	O
a	O
perceived	O
quantity	O
and	O
subject	O
to	O
its	O
own	O
illusions	B-Application
;	O
research	O
indicates	O
that	O
in	O
the	O
tau	B-Application
effect	I-Application
,	O
perceived	O
stimulus	O
spacing	O
follows	O
perceived	O
(	O
phenomenal	O
)	O
time	O
rather	O
than	O
actual	O
(	O
physical	O
)	O
time	O
.	O
</s>
<s>
The	O
tau	B-Application
effect	I-Application
can	O
occur	O
with	O
visual	O
,	O
auditory	O
,	O
or	O
tactile	O
stimuli	O
.	O
</s>
<s>
In	O
touch	O
,	O
the	O
tau	B-Application
effect	I-Application
was	O
first	O
described	O
by	O
Gelb	O
(	O
1914	O
)	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
unimodal	O
(	O
i.e.	O
,	O
purely	O
visual	O
,	O
auditory	O
,	O
or	O
tactile	O
)	O
tau	B-Application
effect	I-Application
,	O
crossmodal	O
tau	B-Application
effects	I-Application
can	O
occur	O
.	O
</s>
<s>
(	O
2008	O
)	O
showed	O
that	O
the	O
time	O
intervals	O
between	O
auditory	O
tones	O
could	O
affect	O
subjects	O
 '	O
perceptual	O
judgements	O
of	O
the	O
spatial	O
interval	O
between	O
visual	O
flashes	O
in	O
a	O
manner	O
consistent	O
with	O
that	O
predicted	O
by	O
the	O
tau	B-Application
effect	I-Application
.	O
</s>
<s>
It	O
is	O
logical	O
,	O
then	O
,	O
to	O
consider	O
that	O
the	O
tau	B-Application
effect	I-Application
occurs	O
as	O
a	O
consequence	O
of	O
the	O
brain	O
's	O
assumption	O
regarding	O
stimulus	O
velocity	O
.	O
</s>
<s>
Indeed	O
,	O
different	O
theories	O
regarding	O
the	O
brain	O
's	O
expectations	O
about	O
stimulus	O
velocity	O
have	O
been	O
put	O
forward	O
in	O
an	O
effort	O
to	O
explain	O
the	O
tau	B-Application
effect	I-Application
.	O
</s>
<s>
The	O
expectation	O
that	O
stimuli	O
tend	O
to	O
move	O
slowly	O
results	O
in	O
the	O
perceptual	O
underestimation	O
of	O
the	O
spatial	O
separation	O
between	O
rapidly	O
consecutive	O
stimuli	O
(	O
"	O
perceptual	O
length	O
contraction	O
"	O
)	O
,	O
thereby	O
reproducing	O
the	O
tau	B-Application
effect	I-Application
and	O
related	O
illusions	B-Application
.	O
</s>
<s>
Modeling	O
the	O
tau	B-Application
effect	I-Application
that	O
occurs	O
in	O
the	O
perception	O
of	O
3-tap	O
sequences	O
,	O
Goldreich	O
and	O
Tong	O
(	O
2013	O
)	O
compared	O
the	O
Bayesian	O
model	O
with	O
a	O
low-speed	O
expectation	O
to	O
a	O
Bayesian	O
model	O
with	O
a	O
low-acceleration	O
expectation	O
—	O
similar	O
to	O
the	O
constant-velocity	O
hypothesis	O
.	O
</s>
<s>
They	O
found	O
that	O
the	O
low-speed	O
prior	O
model	O
provided	O
better	O
fits	O
to	O
the	O
human	O
tactile	O
tau	B-Application
effect	I-Application
data	O
.	O
</s>
<s>
When	O
time	O
is	O
inaccurately	O
perceived	O
(	O
i.e.	O
,	O
because	O
of	O
the	O
kappa	B-Application
effect	I-Application
)	O
,	O
the	O
Bayesian	O
observer	O
model	O
judges	O
stimulus	O
spacing	O
to	O
follow	O
perceived	O
time	O
rather	O
than	O
actual	O
time	O
,	O
consistent	O
with	O
reports	O
from	O
human	O
subjects	O
.	O
</s>
<s>
A	O
spatial	O
perceptual	O
illusion	B-Application
that	O
seems	O
to	O
be	O
closely	O
related	O
to	O
the	O
tau	B-Application
effect	I-Application
is	O
the	O
rabbit	O
illusion	B-Application
.	O
</s>
<s>
In	O
the	O
tactile	O
rabbit	O
illusion	B-Application
,	O
a	O
rapid	O
sequence	O
of	O
taps	O
delivered	O
first	O
near	O
the	O
wrist	O
and	O
then	O
near	O
the	O
elbow	O
creates	O
the	O
sensation	O
of	O
sequential	O
taps	O
hopping	O
up	O
the	O
arm	O
from	O
the	O
wrist	O
towards	O
the	O
elbow	O
,	O
although	O
no	O
physical	O
stimulus	O
was	O
applied	O
between	O
the	O
two	O
actual	O
stimulus	O
locations	O
.	O
</s>
<s>
Like	O
the	O
tau	B-Application
effect	I-Application
,	O
the	O
rabbit	O
illusion	B-Application
has	O
been	O
observed	O
not	O
just	O
in	O
touch	O
,	O
but	O
also	O
in	O
audition	O
and	O
vision	O
.	O
</s>
<s>
If	O
observers	O
interpret	O
rapid	O
stimulus	O
sequences	O
in	O
light	O
of	O
an	O
expectation	O
regarding	O
velocity	O
,	O
then	O
it	O
would	O
be	O
expected	O
that	O
not	O
only	O
spatial	O
,	O
but	O
also	O
temporal	O
illusions	B-Application
would	O
result	O
.	O
</s>
<s>
This	O
indeed	O
occurs	O
in	O
the	O
kappa	B-Application
effect	I-Application
:	O
When	O
the	O
temporal	O
separation	O
between	O
stimuli	O
is	O
constant	O
and	O
the	O
spatial	O
separation	O
is	O
varied	O
,	O
the	O
observer	O
's	O
temporal	O
interval	O
judgment	O
is	O
influenced	O
by	O
the	O
spatial	O
distance	O
between	O
consecutive	O
stimuli	O
.	O
</s>
<s>
The	O
kappa	B-Application
effect	I-Application
is	O
therefore	O
the	O
temporal	O
perceptual	O
analog	O
of	O
the	O
tau	B-Application
effect	I-Application
.	O
</s>
<s>
Goldreich	O
(	O
2007	O
)	O
linked	O
the	O
tau	O
,	O
rabbit	O
,	O
and	O
kappa	B-Application
effects	I-Application
to	O
the	O
same	O
underlying	O
expectation	O
regarding	O
movement	O
speed	O
.	O
</s>
<s>
Goldreich	O
(	O
2007	O
)	O
termed	O
these	O
two	O
fundamental	O
perceptual	O
distortions	O
"	O
perceptual	O
length	O
contraction	O
"	O
(	O
tau	B-Application
effect	I-Application
,	O
rabbit	O
illusion	B-Application
)	O
and	O
"	O
perceptual	O
time	O
dilation	O
"	O
(	O
kappa	B-Application
effect	I-Application
)	O
in	O
analogy	O
with	O
the	O
physical	O
length	O
contraction	O
and	O
time	O
dilation	O
of	O
the	O
theory	O
of	O
relativity	O
.	O
</s>
