Atten Percept Psychophys (2014) 76:230–246
DOI 10.3758/s13414-013-0549-3
Does the human odometer use an extrinsic or intrinsic metric?
Elizabeth R. Chrastil & William H. Warren
Published online: 3 October 2013
# Psychonomic Society, Inc. 2013
Abstract It is commonly assumed that path integration is
based on an extrinsic measure of the objective distance traversed during locomotion. In contrast, biological odometers
may rely on embodied intrinsic measures, such as idiothetic
information specific to an action mode. We investigated this
question using a distance reproduction task in which participants traveled an outbound distance and then reproduced that
distance using the same or a different action mode. The extrinsic model predicted that distance reproduction should be invariant across action modes, whereas the intrinsic model predicted
invariance only within an action mode. In Experiment 1, we
held the outbound mode constant while varying the response
mode (walk–walk, walk–throw) and corrected for response
production error (view–walk, view–throw). In Experiment 2,
we crossed different gaits in the outbound and response modes
(walk, gallop). In both cases, we found that distance reproduction was significantly more accurate when the outbound and
response modes matched, consistent with the intrinsic model.
The results indicate that the human odometer preferentially
relies on an intrinsic, rather than an extrinsic, metric. This
solution is sufficient to support successful path integration
within an action mode (but not across action modes), without
the difficulties of objective distance estimation.
Keywords Perception and action . Navigation . Locomotion
Path integration, also known as dead reckoning, refers to the
ability to keep track of one’s position and orientation in the
environment by temporally integrating information about selfmotion. Accurate path integration implies that an animal could
walk a circuitous outbound path from a home location and
then take a direct path back to its starting point, a behavior
known as homing. Animals such as desert ants are indeed
capable of remarkably accurate and precise homing (Müller &
Wehner, 1988; Sommer & Wehner, 2004; Wehner & Wehner,
1986), although homing performance in humans indicates that
path integration is biased and more variable (Chance, Gaunet,
Beall, & Loomis, 1998; Kearns, Warren, Duchon, & Tarr,
2002; Klatzky et al., 1990; Loomis et al., 1993; Peruch,
May, & Wartenberg, 1997). Although error patterns in human
path integration have been well studied, the underlying processes remain unclear.
Fujita, Klatzky, Loomis, and Golledge (1993) identified
three component processes in homing tasks: (1) encoding the
distances and angles traversed on the outbound path, (2) integrating those distances and angles to compute a homebound
trajectory or homing vector, and (3) executing that homebound
path. The authors argued that error may be associated with
each component. This analysis raised a number of questions
that remain outstanding. First, what exactly is encoded on the
outbound path; that is, what is the metric of path integration?
Second, what is the source of the path integration errors
observed in human homing, and can they be parsed into
encoding, integration, and execution errors? Third, what is
the nature of the integration process; for example, is the homing vector derived via a trigonometric computation or a heuristic process? Before the latter questions can be answered, the
first needs to be addressed; in this article, we will focus on the
problem of distance measurement, or odometry.
The distance metric of the human odometer
E. R. Chrastil : W. H. Warren
Cognitive, Linguistic & Psychological Sciences, Brown University,
Providence, RI, USA
E. R. Chrastil (*)
Psychology Department, Boston University, 2 Cummington Mall,
Boston, MA 02215, USA
e-mail: chrastil@bu.edu
First, consider the metric of path integration. It is often assumed that path integration encodes the objective distances
and angles that an animal traverses through the environment,
using an extrinsic metric—that is, an absolute measure, defined in objectively scaled units. But there is no reason to
believe a priori that biological systems evolved to extract
Atten Percept Psychophys (2014) 76:230–246
environmental properties as measured by pre-19th-century
geometers, such as linear distances in Euclidean space.
Rather, biological systems may measure behaviorally relevant properties using an embodied intrinsic metric—that is,
a relational measure in action-scaled units that are specific
to the action involved (Gibson, 1979; Warren, 1984, 2007).
As was first suggested by Bishop Berkeley (1709/2010),
distance may be “measured by motion of the body” as a
tangible locomotor interval. Subsequent research has
shown that simple locomotor units such as the number of
steps, step length, elapsed time, or expended energy are
inadequate to characterize the odometer, and it is likely that
the system depends on a higher-order complex of idiothetic
variables (Durgin, Akagi, Gallistel, & Haiken, 2009;
Mittelstaedt & Mittelstaedt, 2001; Schwartz, 1999; Turvey,
et al., 2009; Wittlinger, Wehner, & Wolf, 2006, 2007).
To investigate this question, we operationalized two conceptual models of distance encoding by the human odometer
and tested them in a distance reproduction task. In a standard
distance reproduction task, the participant walks a specified
distance on an outbound path and is then asked to walk an
equivalent distance on the response path. The extrinsic model
proposes that objective distance (physical distance in the
world) is encoded on the outbound path and then produced
on the response path. This model predicts that distance reproduction should be invariant over changes in action mode, once
execution error is controlled for. The intrinsic model proposes
that an action-scaled measure based on idiothetic (motor commands, proprioceptive input, and vestibular input) information
is registered on the outbound path and then reproduced on the
response path. On this view, distance reproduction would be
invariant only over actions that possess the same intrinsic
metric, so that performance should be best when the outbound
and response modes match. The intrinsic model still permits
accurate distance reproduction and homing, provided that the
same action mode is maintained during travel, without a
strong assumption of objective distance measurement. We
tested these predictions using a distance reproduction task in
which the action mode changed between the outbound and
response paths.
Encoding and execution error
Next, consider the three possible sources of path integration
error identified by Fujita et al. (1993): encoding error,
integration error, and execution error. The authors reasoned that execution error makes only a small contribution
to the overall error, on the basis of the finding that blind
walking to a target is quite accurate (Elliott, 1986, 1987;
Loomis, da Silva, Fujita, & Fukusima, 1992; Ooi, Wu, &
He, 2001; Philbeck & Loomis, 1997; Thomson, 1983). In
the standard blind-walking task, also called visually
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directed walking , a participant views a target, closes his
or her eyes, and then walks to the target location. Since the
target distance is given visually, the task eliminates locomotor encoding error, so the authors argued that blindwalking performance provides a measure of execution error. Furthermore, they assumed that integration error in
computing the homebound path is negligible. Thus, Fujita
et al. (1993) concluded that the primary source of error in
path integration is encoding error, as summarized in their
encoding-error model.
Following this logic, researchers have estimated encoding
error using distance and angle reproduction tasks (Jürgens,
Boß, & Becker, 1999; Klatzky et al., 1990; Loomis et al.,
1993; Marlinsky, 1999; Schwartz, 1999). Assuming that the
traversed distance is encoded on the outbound path, and that
little execution error occurs on the response path, then the
overall reproduction error—the error in traveling a distance
and then reproducing that distance—can be interpreted as a
measure of encoding error. For example, an overshoot on the
response path would indicate an overestimate of the distance
during encoding, and vice versa.
However, blind walking does not necessarily provide a
valid estimate of execution error, and hence distance reproduction may not offer a valid estimate of encoding error. In
blind walking, it is possible that both visual distance perception and locomotor execution are inaccurate, but compensatory. Suppose that the visual–motor system has established a
calibration between visually perceived distance and locomotor
displacement (Rieser, Pick, Ashmead, & Garing, 1995).
Thanks to this calibration, blind-walking performance could
be quite accurate, despite large perceptual and execution errors. For example, if distance were visually underestimated
and locomotor execution produced overshooting, these errors
would cancel out to yield accurate blind walking. Thus, performance in the standard blind-walking task cannot be taken
as a measure of either perceptual accuracy or execution error.
Recognizing this problem, researchers have developed other
tasks, such as indirect walking or continuous pointing, in
which the ability to walk to a perceived location cannot be
explained by a simple calibration (Campos, Siegle, Mohler,
Bülthoff, & Loomis, 2009; Loomis, Klatzky, Philbeck, &
Golledge, 1998; Loomis & Philbeck, 2008; Philbeck, Loomis,
& Beall, 1997). However, errors on indirect paths tend to
differ from those on direct paths (Philbeck et al., 1997), and
it remains possible that the standard blind-walking task is
based on a visual–locomotor calibration. Thus, we question
whether the execution error of walking has been firmly
established.
Moreover, the notion that blind walking provides an estimate of pure execution error presumes that the locomotor
response is preplanned and ballistic. That is, it presumes that
the response is executed without simultaneously encoding the
traversed distance on the response path. But it seems highly
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likely that the locomotor system is continuously registering
idiothetic information for travel distance, and unlikely that the
system would ignore such information on the response path
when it could be used to confirm that the intended distance is
actually being reproduced. Thus, performance in a blindwalking task cannot be taken as a measure of pure execution
error, because it may also reflect encoding error during the
response. We will refer to the combined source of encoding
and execution error during a response as production error.
Consequently, the standard distance reproduction task may
not provide a valid estimate of encoding error. First, if execution error cannot be neglected, the reproduction error might
confound encoding error on the outbound path with execution
error on the response path. Second, if distance encoding
occurs on both the outbound and response paths, reproduction
would include both types of encoding error. In sum, it may not
be possible to disentangle encoding error from execution error
in a standard reproduction task. However, we can estimate
relative encoding error by manipulating the action modes on
the outbound and response paths.
Extrinsic and intrinsic models
This brings us back to the issue of the path integration metric.
Models of path integration generally assume that the human
odometer encodes objective distance during locomotion
through the environment (e.g., Fujita et al., 1993; Mittelstaedt
& Mittelstaedt, 2001). Alternatively, the odometer might register intrinsic action-scaled information during locomotion
and reproduce it on the response path. Here we detail these
alternatives and explain their predictions for distance reproduction. Although it is theoretically possible that both extrinsic and intrinsic models might have ballistic versions, we think
it unlikely for the reasons described above, so we will focus on
matching models in which information is monitored during
both the outbound and response paths.
Extrinsic models In an extrinsic model, the objective distance
traveled on the outbound path is encoded and stored; during
the response, objective distance is also encoded, and locomotion continues until this value matches the stored value
(Fig. 1a). On this model, errors might occur due to (1) distance
encoding on the outbound path, (2) decay of the stored distance value, (3) distance encoding on the response path, and
(4) comparison of the stored distance value with the response
value.
The extrinsic model predicts that once the outbound distance is encoded, performance should not depend on the
action mode used to produce the same distance during the
response. Although distance is presumably not measured in
feet or meters, the extrinsic model proposes that objective
distance (the physical distance in the world) is mapped into
Atten Percept Psychophys (2014) 76:230–246
some internal quantity that provides a common “yardstick”
across different action modes. For example, in gaits with a
double-support phase such as walking, if leg length is known
and the angle between the two legs during double-support is
given by proprioception, then step length can be determined,
and the traversed distance could be registered by a “stride
integrator,” independent of speed. A different mechanism
might apply in single-support gaits such as skipping (e.g., a
mechanism based on leg angle and impulse at kickoff), but it
likewise maps objective distance into the same common metric, which could also be used to control other actions such as
throwing. Thus, different action modes are calibrated to each
other because they encode the same objective distance.
Consequently, the extrinsic model predicts that the constant
error in distance reproduction should be unaffected by the
match between the outbound and response modes. Obviously,
different types of responses may have different accuracies, so
when testing the prediction we correct for this by measuring
the production error of the response alone and subtracting it
from the overall reproduction error. This computation yields
an estimate of the encoding error in the outbound mode. The
extrinsic model predicts that this estimated encoding error
should be independent of the response mode, because objective distance is encoded and reproduced regardless of the
particular action that carries it out.
Mittelstaedt and Mittelstaedt (2001) proposed such a
distance-matching model, in which an idiothetic transfer function encodes a representation of distance traversed on the
outbound path, and a similar independent function encodes
distance traversed on the response path, until the difference
between them is brought to zero. Note that this model presupposes that the purpose of the transfer function is to convert
idiothetic information into a measure of objective distance. If
such a transfer function is linear with a constant gain, then
distance reproduction will be invariant over a variety of outbound and response conditions. Contrary to this expectation,
Mittelstaedt and Mittelstaedt reported systematic reproduction
errors when walking speed was changed between the outbound and response path. Specifically, constant errors were
lowest when the outbound and response speeds were the
same, but significantly higher when the walking speeds differed. Nevertheless, they explained this effect within the extrinsic framework, proposing that the idiothetic transfer function is nonlinear (a leaky integrator), with parameters that
depend on walking speed.
In our view, to claim that different actions have different
transfer functions—in essence, that each action mode possesses its own “yardstick” for measuring distance—implies
that objective distance is not internally represented. The claim
that distance is encoded differently in each action mode reduces to the claim that what is encoded is intrinsic (modespecific) information, not extrinsic distance. If distance reproduction is not invariant across action modes, this implies that
Atten Percept Psychophys (2014) 76:230–246
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Fig. 1 Comparison of the two models. a In the extrinsic model, as an
observer walks forward, the objective distance is encoded as an internal
quantity in common units; the observer then walks back until the same
distance is produced. Note that the production error on the response path
may include both execution error and encoding error during the response,
but these two errors cannot be dissociated. b In the intrinsic model, an
observer walks forward, registering some action-scaled idiothetic quantity, and then walks back until the idiothetic quantity is dissipated or
matched
there is no common metric for objective distance. We propose
to take the distance-matching model one step farther, by
suggesting that no representation of extrinsic distance may
exist at all, but merely the matching of intrinsic idiothetic
information.
outbound path and idiothetic information associated with
running on the response path, nothing would guarantee that
the same objective distance would be traversed. Moreover,
this quantity would not readily used to control other actions
such as throwing. It is possible that different action modes
become mutually calibrated through experience, such as repeated travel between two locations using different gaits, or
throwing and walking to retrieve the projectile, but that this is
contingent on specific experience. Thus, the intrinsic model
predicts that the estimated encoding error should depend on
the response mode, for reproduction error would be smaller
when the outbound and response modes matched.
Previous research has indicated that mismatches between the outbound and response modes tend to yield larger
constant reproduction errors, as expected by the intrinsic
model. Schwartz (1999) manipulated the step length and
step frequency of walking on the outbound path and asked
participants to return to the starting point at a normal walk,
over a distance range of 10 to 50 m. When the step lengths
of the outbound and response modes differed, the response
range was compressed and absolute errors increased, relative to the normal walk–walk condition.1 Interestingly,
Schwartz reported that the walking speed on the response
path was correlated with the prescribed speed on the outbound path, even though participants were instructed to
return at a normal walk. This observation suggests that they
were attempting to match the outbound and response gaits,
perhaps in order to match the idiothetic information.
Intrinsic models In an intrinsic model, action-scaled information is registered on the outbound path as a measure of
locomotor displacement, and action-scaled information is
also registered on the response path until the outbound
value is matched (Fig. 1b). For example, suppose that some
idiothetic quantity is accumulated during the outbound
path, depending on the action mode. During the response,
another idiothetic quantity is accumulated by a similar
process until the outbound value is matched (or a reciprocal
process dissipates the accumulated value until it goes to
zero). To the extent that the mappings between distance and
idiothetic information were the same in the outbound and
response modes, the objective distance would be reproduced. This model suggests that errors may occur in
(1) the accumulation of idiothetic information on the outbound path, (2) decay of the stored idiothetic value, (3) the
accumulation (or dissipation) process on the response path,
and (4) the comparison of two accumulated values.
The predictions of the intrinsic model contrast with those of
the extrinsic model. Specifically, according to this model one
would expect that constant errors in distance reproduction
would be smaller when a participant used the same action
mode on the outbound and response paths, once response
accuracy was controlled for. If the navigator were to register
idiothetic information associated with walking on the
1
Schwartz (1999) concluded that an effect of step frequency was mediated by its influence on step length.
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Schwartz concluded that distance reproduction is based on
a complex of proprioceptive variables that does not simply
correspond to a stride integrator.
Turvey et al. (2009) extended these findings to different
gaits. In contrast to Schwartz, they found that differing speeds
on the outbound path did not affect reproduction distance on
the response path. They did find, however, that galloping or
performing a hesitation step on the outbound path reduced
accuracy when walking on the response path. Turvey et al.
(2009; Turvey, Harrison, Frank, & Carello, 2012) proposed
that different gaits fall into specific symmetry classes
(Golubitsky, Stewart, Buono, & Collins, 1999; Pinto &
Golubitsky, 2006), and only gaits within the same class allow
accurate distance reproduction.
Sun, Campos, Young, Chan, and Ellard (2004) crossed
visual information and idiothetic information on the outbound
and response phases, yielding four conditions: view–view
(visual matching), view–walk (blind walking), walk–walk
(standard distance reproduction), and walk–view. Conditions
with matching outbound and response modes (view–view and
walk–walk) tended to have the lowest constant errors, whereas
mismatching conditions (view–walk and walk–view)
yielded large errors, consistent with the intrinsic model.
However, an exception occurred when they added visual
information during walking (Sun et al., 2004). Walking
with vision on both outbound and response paths (walk–
walk with vision) led to significant errors. Walking with
vision on the response path only (view–walk with vision)
led to overshooting the target distance, whereas vision on
the outbound path only (walk with vision–view) led to
undershooting. These findings suggest that visual information such as optic flow may result in an underestimation of
traversed distance and interfere with matching idiothetic
information on the outbound and response paths (see also
Bremmer & Lappe, 1999; Campos, Byrne, & Sun, 2010;
Frenz, Bremmer, & Lappe, 2003; Harris, Jenkin, &
Zikovitz, 2000; Lappe, Jenkin, & Harris, 2007; Mossio,
Vidal, & Berthoz, 2008; Redlick, Jenkin, & Harris, 2001).
The potential interaction of visual and idiothetic information in the human odometer needs further exploration.
Finally, research on visual and vestibular information also
implies that objective distance may not be encoded. Rather
than rely on distance, participants may rely on the velocity
profile of the outbound and return paths, matching them
whenever possible (Berthoz, Israël, George-Francois, Grasso,
& Tsuzuku, 1995; Bremmer & Lappe, 1999; Glasauer,
Schneider, Grasso, & Ivanenko, 2007; Grasso, Glasauer,
Georges-François, & Israël, 1999; Israel & Berthoz, 1989;
Israel, Chapuis, Glasauer, Charade, & Berthoz, 1993; Israel,
Grasso, Georges-François, Tsuzuku, & Berthoz, 1997). These
findings are consistent with the intrinsic model, in that participants reproduce the spatiotemporal dynamics of the outbound
path rather than using a distance metric.
Atten Percept Psychophys (2014) 76:230–246
In sum, the previous literature suggests that matching the
outbound and response modes facilitates distance reproduction, consistent with an intrinsic model of distance reproduction. These experiments have tested numerous mismatches in speed, step length, gait, and velocity profile.
The findings suggest that the idiothetic information on the
outbound and response paths must match fairly closely for
accurate distance reproduction to be observed. In the present study, we tested very different action modes, such as
throwing.
Although the previous literature has shown that matched
outbound and response modes tend to yield more accurate
distance reproduction, they have not successfully estimated
the potential sources of error. In particular, prior attempts to
measure and directly compare encoding error have proven
inconclusive. Thus, there has yet to be a strong test of
alternative models of path integration. The aims of the
present study were (1) to establish whether the human
odometer encodes extrinsic distance or intrinsic actionscaled information and (2) to derive a useful estimate of
encoding error.
Logic of the experiments
The two experiments presented here were designed to test
whether the metric of the human odometer is extrinsic or
intrinsic by manipulating the match between outbound and
response modes in a distance reproduction task. In the first
experiment, we held the outbound action mode constant while
varying the response mode, whereas in the second we crossed
the outbound mode and the response mode.
Previous experiments have typically manipulated the outbound mode while keeping the response measure constant.
Although this makes good sense, it also has a drawback:
Encoding accuracy in the outbound mode is not controlled,
so a difference in performance might be due to a difference in
encoding error rather than to the match between the outbound
and response modes. An alternative would be to hold the
outbound mode constant and manipulate the response mode.
The obvious drawback here is that response accuracy is not
controlled, and may differ between response modes; thus, one
must estimate and correct for production error during the
response. In the present study, we pursued both of these
approaches in order to obtain converging measures of performance with matching and mismatching action modes.
In Experiment 1, we held the outbound mode constant and
varies the response mode while controlling for differences in
production. In Experiment 2, we fully crossed the outbound
mode and the response mode. These two experiments would
enable us to determine whether distance reproduction improves when the outbound and response modes match, as is
predicted by the intrinsic model.
Atten Percept Psychophys (2014) 76:230–246
Experiment 1
The extrinsic model predicts that objective distance is encoded
and should transfer to other responses, whereas the intrinsic
model predicts that performance should be more accurate
when the outbound and response modes match. In Experiment
1, we held the outbound mode constant and varied the response mode, yielding two distance reproduction conditions:
walk–walk and walk–throw. However, we also had to control
for the possibility that people are worse at throwing a given
distance than walking it. We thus measured the difference in
production error between walking and throwing in two additional conditions—view–walk and view–throw—and used the
result to correct the reproduced distances. The extrinsic model
predicts that this correction should completely account for the
difference between walk–walk and walk–throw: If the outbound distance is encoded in the same way, the only source of
error would be the production error. In contrast, the intrinsic
model predicts that reproduction errors in the walk–walk
condition will still be smaller than those in the walk–throw
condition, even after the correction: When the action modes
match, the outbound idiothetic information can be matched
during the response, but this information cannot be used to
control throwing accurately, because it does not encode
distance.
The correction for walking and throwing accuracy amounts
to subtracting production error from total reproduction error.
This subtraction is equivalent to estimating the encoding error
on the outbound path (see below). We performed two such
estimates, one in which the outbound and response modes
matched (walk–walk) and one in which they did not (walk–
throw). The extrinsic model predicts that these two estimates
of encoding error would be the same, because objective distance would be encoded and reproduced, whereas the intrinsic
model predicts that they would differ, because no common
distance metric would be present. In particular, the transfer of
idiothetic information from walking to throwing might result
in increased error as compared to a walking response, in which
the idiothetic information could be matched. The extrinsic
model thus predicts that the estimates of encoding error should
be the same, regardless of the response mode, whereas the
intrinsic model predicts that the estimated encoding errors
would depend on the response mode. Experiment 1 provided
a test of these predictions.
Model predictions
The computation of reproduction error, corrected for differences in production, makes the following assumptions: (1)
Constant errors are additive; that is, errors from different
sources, such as encoding or production error, can be summed
linearly to yield total reproduction error. (2) Encoding error
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when viewing a target is the same, regardless of the response
mode.
The extrinsic model predicts that distance reproduction
should be accurate (after correction for production error)
whether or not the action modes match, whereas the intrinsic
model predicts more accurate distance reproduction when the
outbound and response modes are the same than when they
differ. In order to determine whether distance reproduction
depends on the match between the outbound and response
modes, in Experiment 1 we held the outbound mode constant
and varied the response mode (walk–walk and walk–throw),
while controlling for differences in response accuracy. Specifically, we corrected the overall reproduction error by
subtracting a measure of production error (view–walk and
view–throw), as follows.
As is illustrated in Fig. 1a, the constant error in distance
reproduction (REPRO) is the sum of the encoding error on the
outbound path (ENCout) and the production error on the
response path (PROD):
REPRO ¼ ENC out þ PROD:
ð1Þ
Note that production error includes both execution error
(EX) and encoding error during the response (PROD = EX +
ENCresp).2
Although we cannot measure execution or encoding
errors directly, we can measure reproduction and production errors. Once reproduction errors are corrected
for any difference in production, they can be used to
test the extrinsic and intrinsic models. In particular,
these corrected reproduction errors yield estimates of
the encoding error (ÊNCout), as can be seen by rearranging
Eq. 1:
b out ¼ REPRO−PROD:
ENC
ð2Þ
We will compare two such estimates of encoding
error, one in which the outbound and response modes match,
and one in which they differ (refer to Fig. 2b). First, we
measure overall reproduction error when the action modes
match (walk–walk) and when they do not (walk–throw).
Second, because throwing ability might simply be poorer than
walking ability, we measure the production errors for both
walking (view–walk) and throwing (view–throw). A difference between these conditions would be due to a difference
between walking and throwing accuracy. Finally, we correct
for any difference in production accuracy by computing two
2
Substituting for PROD, we see that REPRO = ENCout + (EX +
ENCresp). Interestingly, if the outbound and response encoding processes
are indeed the same, the encoding errors would cancel, such that ENCresp
= −ENCout, and the reproduction error would simply reflect residual
execution error, REPRO = EX.
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Fig. 2 a View of the experimental setup and materials. b Conditions in Experiment 1, illustrating how reproduction errors (left) were corrected for
production errors (center), yielding two estimates of encoding error (right)
estimates of the outbound encoding error.3 The first subtracts
the production error for walking from the overall reproduction
error [(walk–walk) – (view–walk)]:
b ww ¼ REPROww −PRODw :
ENC
ð3Þ
The second estimate subtracts the production error for
throwing from the reproduction error [(walk–throw) –
(view–throw)]:
b wt ¼ REPROwt −PRODt :
ENC
3
ð4Þ
Our purpose here was to compare these two estimates of encoding error;
we are not claiming that the estimates are accurate. The computations
assume that the encoding error when viewing the target is the same
whether the response is walking or throwing (although they do not assume
that the encoding error is zero). Thus, production errors after viewing a
target are somewhat different from those in distance reproduction when
walking: PRODv = ENCv + ENCresp + EX. Because we assume that the
encoding error for viewing is the same regardless of the response mode, we
can safely subtract production errors in order to compare the encoding
errors. However, this estimate of encoding error may include a component
ENCv that does not reflect the actual encoding error for walking.
A difference between these two estimates (ÊNCww < ÊNCwt)
would indicate that the overall reproduction error is smaller
when the outbound and response modes match, even after
correcting for differences in production error, consistent with
the intrinsic model.
The actual encoding error in walk–walk is presumably the
same as in walk–throw. However, the models make different
predictions regarding the two estimates of encoding error. The
extrinsic model predicts that distance reproduction should be
independent of the response mode; hence, the estimated
encoding error should be as well. In contrast, the intrinsic
model predicts that distance reproduction should be most
accurate, and the estimated encoding error smaller, when the
outbound and response modes match.
Method
Participants A group of 20 participants took part in Experiment 1 (ten male, ten female; age 24.05 ± 5.987 years, range
19–43); three additional participants failed to complete all
Atten Percept Psychophys (2014) 76:230–246
experiment sessions and were not included in the analysis.
They all had normal or corrected-to-normal vision. All participants gave informed consent to participate in the study in
accordance with the Brown University Institutional Review
Board.
Stimuli and setup The experiment was composed of a total of
four conditions, with 50 trials in each: walk–walk, walk–
throw, view–walk, and view–throw. Trials were blocked by
condition and presented within subjects during three experimental sessions, along with the conditions for Experiment 2b
and one other condition not presented here.
In the walking condition, strips of foam (approximately
4.5 cm wide and 1.5 cm high) were attached to the carpeted
floor with Velcro and used to guide participants on a
straight path (Fig. 2a). Participants held a cane made of
plastic tubing (4-cm diameter) with a wiffle ball attached to
the bottom to create a smooth foot. They stood approximately 36 cm to the left of the foam guide, grasped the cane
with their right hand, and held it against the right side of the
strip to guide their walking direction. To indicate where to
stop when walking, another foam strip crossed over the
first; when participants felt the cane touch this junction, it
signaled them to stop. Audio cues also instructed participants when to start and stop walking.
For the throwing condition, a beanbag (approximately
50 g) was covered with patches of Velcro to minimize sliding
after it hit the carpeted floor and to keep it in its landing
location. Two participants preferred to throw the beanbag with
their left hand, and the rest used their right hand.
In the view condition, the visual target was a vertical section
of white PVC pipe (approximately 8.5 cm high and 10.5 cm in
diameter), which was chosen to avoid a familiar size cue. Other
distance information was preserved, including declination angle, motion parallax, binocular stereopsis, vergence, accommodation, and relative size across trials. For this condition,
only a single foam strip in the orthogonal direction remained
on the floor to guide responses, while the single “outbound”
foam track in the target direction remained in place.
The participant’s head position was tracked using an IS900
hybrid sonic/inertial tracking system (InterSense, Billerica,
MA), hosted by a Dell XPS 730X computer. The experimenter’s head position was also tracked, as a means of recording the landing location of the beanbag. A wireless mouse
was used to mark the beginning and end of each response in
the position data file. Audio cues were presented through two
loudspeakers driven by the computer’s sound system, and the
participant wore headphones to reduce external noise.
Procedure After giving informed consent, participants received practice walking with their eyes open and closed along
the foam guides and practice throwing a beanbag to targets
with their eyes open. The practice targets were colored rolls of
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gaffer tape placed at different distances from those in the test
phase, over a similar range; the experimenter called out a
target color in a random order until each had been practiced
five times. Participants were instructed to throw the beanbag
while standing on two feet, and if they needed to throw farther,
they should bend their knees more and arc the throw higher.
Finally, participants were given two practice trials at the
beginning of each experimental condition to familiarize themselves with the procedure, again at nontest distances but over a
similar range.
Distance encoding by counting steps or intervals was minimized by presenting a simple arithmetic problem during the
“outbound” phase of each test trial, generated by randomly
adding, subtracting, or multiplying the digits 2 through 9. In
the walk conditions, an experimenter gave one arithmetic
problem just after the participant started walking. In the view
conditions, an experimenter gave one problem after the participant had viewed the target and put on a blindfold. In
addition, participants were instructed that they might be
tempted at times to count their steps, but they were asked to
refrain from counting as the experimenters were not interested
in how well they could count steps.
Five outbound distances were used in each of the four
conditions: 2, 4, 5, 6, and 8 m. Participants completed ten trials
at each distance in a random order, yielding 50 trials per condition, for a total of 200 trials. Trials were blocked by condition,
and the order of the blocks was randomized for each participant.
Participants completed all four blocks as part of three 1.5-h
sessions, two blocks per session, for a within-subjects design.
At the end of each session, they filled out a brief questionnaire,
in which they described any strategies they might have used, and
rated the difficulty of each of the tasks on a 1–7 scale.
Four experimental conditions were compared in this experiment: walk–walk, walk–throw, view–walk, and view–throw
(Fig. 2b). These conditions were created by crossing two
outbound modes (view and walk) with two response modes
(walk and throw).
Walk–walk This condition measured the reproduction error
for walking (REPROww). Participants wore a blindfold during
the entire block of trials. An audio cue (“Go”) directed participants to start walking. They walked forward while
blindfolded until the cane touched one of the crossing foam
strips and they heard a loud beep, indicating that they should
stop walking and turn 90º to the left. After a 7-s pause, in
which they turned and the cane was set on the next guide strip,
another audio cue (“Go”) directed them to start walking again.
Participants were instructed to walk the same distance along
the new guide as they had walked on the first one. When they
judged that they had travelled the same distance, participants
stopped and clicked the mouse, at which point their position
was recorded and a chime sounded. An experimenter guided
the participant back to the starting location.
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Walk–throw This condition measured the reproduction error
when walking is reproduced by throwing (REPROwt). The
procedure was identical to that of walk–walk except that after
the 7-s pause, during which they turned 90º, participants were
instructed to throw the beanbag the same distance they had
walked on the first track. An experimenter recorded the position of the beanbag. A chime sounded when the position was
recorded, and another experimenter walked the participant
back to the start location. Again, participants kept the blindfold on during the entire block.
View–walk This condition measured the production error for
walking (PRODw). The procedure was identical to that of the
walk–walk condition, except that the outbound distance was
perceived by viewing a target. An audio cue (“Blindfold off”)
directed participants to move the blindfold so that they could
see the target. Participants were allowed to view the target for
5 s, and then an audio cue (“Blindfold on”) played. During the
ensuing 7-s pause, participants were to replace the blindfold
and turn 90º to the left. A final audio cue (“Go”) directed
participants to walk an equivalent distance along a guide strip
in that direction. Participants kept the blindfold on during the
block except when viewing the target.
View–throw This condition measured the production errors
for throwing (PRODt). The procedure was identical to that
of the view–walk condition, except that after viewing the
target, participants were instructed to replace the blindfold,
turn 90º to the left, and, after the 7-s pause, throw the beanbag
an equivalent distance in that direction. Again, they kept the
blindfold on during the block except when viewing the target.
Occasional trials were excluded from the analysis when the
tracker lost the participant’s position, the mouse did not record
the data properly, the participant lost his or her place, or the
beanbag was thrown into a wall or the ceiling. These errors
occurred on fewer than 2 % of the trials. The analysis was
performed on both the response distance (to derive constant
error) and the within-subjects standard deviation of response
distance (variable error) in each condition.
Results and discussion
Initial examination of the absolute (unsigned) errors offers an
overall picture of accuracy in distance reproduction. The mean
absolute errors were walk–walk (M = 0.611 m, SD = 0.206),
walk–throw (M = 1.105 m, SD = 0.419), view–walk (M =
0.727 m, SD = 0.229), and view–throw (M = 0.801 m, SD =
0.427). A two-way repeated measures analysis of variance
(ANOVA) on absolute error found a significant main effect
of outbound distance [F (4, 76) = 16.144, p < .001], a significant effect of condition [F (3, 57) = 4.671, p < .01], and a
significant Condition × Distance interaction [F(12, 228) =
Atten Percept Psychophys (2014) 76:230–246
1.926, p < .05]. A post-hoc test comparing the walk–walk
condition and the walk–throw condition found a significant
difference between the mean absolute errors for these conditions (p < .01). These results suggest that conditions in which
the outbound and response modes match (walk–walk) are
more accurate than those in which they do not match (walk–
throw).
But the result of interest in Experiment 1 was the estimated
encoding error. To obtain this value, we stepped through the
analysis of reproduction error and production error, starting
with the raw distance reproduction data (see Figs. 3 and 4);
errors corresponded to overshooting or undershooting the
diagonal in these figures. The corrected reproduction errors—equivalent to the estimated encoding errors—are represented in Fig. 5.
First, we plotted the mean response distance as a function
of outbound distance in the walk–walk and walk–throw conditions (Fig. 3a). Responses were more accurate (closer to the
diagonal) when the action modes matched (walk–walk;
REPROww) than when they differed (walk–throw; REPROwt),
in which case participants tended to overshoot short distances
and undershoot long distances. A planned two-way repeated
measures ANOVA on response distance revealed a significant
main effect of outbound distance [F(4, 76) = 462.956, p <
.001] and a significant Distance × Condition interaction [F (4,
76) = 38.927, p < .001], confirming that reproduction errors
were significantly smaller when the outbound and response
modes matched. Similarly, an ANOVA on within-subjects
standard deviations also yielded a main effect of distance
[F (4, 76) = 28.997, p < .001) and a significant Distance ×
Condition interaction [F (4, 76) = 3.392, p < .05]. Thus,
variable errors were also lower when the outbound and response modes matched.
A linear regression on the mean response distance
yielded a slope of 0.892 (intercept = 0.411, r = .999) for
the walk–walk condition, as compared to 0.589 (intercept =
1.611, r = .997) for the walk–throw condition (Fig. 3a),
indicating that the range of distance responses was more
compressed in the walk–throw condition. The former value
is in agreement with prior research, which has generally
found quite accurate distance reproduction, with a slight
tendency to overshoot small distances and undershoot large
distances (Klatzky et al., 1990; Loomis et al., 1993;
Marlinsky, 1999; Schwartz, 1999; Turvey et al., 2009).
The latter condition has not been previously studied.
These results suggest that distance reproduction depends
on whether the outbound and response modes match. But
obviously, walking and throwing ability might differ, so the
next step was to estimate production accuracy by plotting the
mean response distance as a function of target distance in the
view–walk (PRODw) and view–throw (PRODt) conditions
(Fig. 3b). Walking responses were quite accurate (close to the
diagonal), whereas throwing responses were compressed.
Atten Percept Psychophys (2014) 76:230–246
Fig. 3 Mean response distance as a function of outbound distance in
Experiment 1. a Overall reproduction performance for walking on the
outbound path and either a walking or throwing response. b Production
accuracy for walking and throwing responses, after viewing the target
distance. The solid gray diagonal lines indicate accurate performance,
whereas overshooting and undershooting correspond to constant error;
error bars represent between-subjects standard errors
A planned two-way repeated measures ANOVA on mean
response distance revealed a significant main effect of target
distance [F (4, 76) = 498.578, p < .001] and a significant
Distance × Condition interaction [F(4, 76) = 8.595, p < .001],
confirming that throwing had a significantly lower production
accuracy than walking. In contrast, a similar ANOVA on the
within-subjects standard deviation showed only a main effect of
distance [F(4, 76) = 34.653, p < .001], indicating that the
precision of these responses is comparable.
Linear regressions on the mean response distance yielded
slopes of 0.976 (intercept = −0.292, r = .999) for the view–
walk condition and 0.793 (intercept = 0.470, r = .999) for the
view–throw condition (Fig. 3b), confirming distance compression for throwing. These results are in line with previous
239
Fig. 4 Mean response distance as a function of outbound distance (data
replotted from Fig. 3). a Performance for the walking response, when
either walking or viewing the outbound distance. b Performance for the
throwing response, when either walking or viewing the outbound distance. The difference between the curves is the estimated outbound
encoding error. Error bars represent between-subjects standard errors
research showing a greater underestimation of large distances
for blind throwing than blind walking (Eby & Loomis, 1987).
In contrast, a study by Sahm, Creem-Regehr, Thompson, and
Willemsen (2005) showed no Distance × Response interaction; however, they only tested distances up to 6 m, whereas
we tested out to 8 m, resulting in a stronger interaction.
Thus, we observed significantly greater production errors
for throwing than for walking. The final step was to use this
result to correct the overall reproduction error by subtracting
the production errors for walking and throwing (refer to
Fig. 2b). This correction yielded two estimates of the outbound encoding error in walking. First, we subtracted the
production error for walking from the overall reproduction
error [(walk–walk) – (view–walk)]; that is, we computed the
difference between the two curves in Fig. 4a (REPROww –
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Fig. 5 Estimated encoding error (corrected reproduction error) as a
function of outbound distance. One estimate is based on the walking
response (ÊNCww), and the other is based on the throwing response
(ÊNCwt); each has been corrected for response production error. Error
bars represent between-subjects standard errors
PRODw = ÊNCww). The resulting estimate of encoding error,
based on the walking response, is plotted in Fig. 5 (filled
symbols). Second, we subtracted the production error for
throwing from the overall reproduction error [(walk–throw)
– (view–throw)]; that is, we computed the difference between
the two curves in Fig. 4b (REPROwt – PRODt = ÊNCwt). This
estimate of encoding error, based on the throwing response, is
also plotted in Fig. 5 (open symbols).
Figure 5 thus represents the two estimates of encoding error
(i.e., corrected reproduction error) as a function of outbound
distance. It is apparent that the estimate from the walk–walk
condition (ÊNCww), when the outbound and response modes
match, is flatter than the estimate from the walk–throw condition
(ÊNCwt), when they differ. A planned two-way repeated measures ANOVA on the two estimates yielded a main effect of
distance [F(4, 76) = 9.817, p < .001] and a significant Distance
× Condition interaction [F(4, 76) = 2.969, p < .05]. This result
indicates that when the outbound and response modes match,
the error range is smaller, whereas when the modes differ, short
distances are more overestimated and long distances are more
underestimated. A similar ANOVA on the within-subjects standard deviations yielded no effects, indicating that variable error
does not depend on matching action modes. This finding suggests that random errors in encoding processes on the outbound
and response paths are uncorrelated.
Linear regressions of the two estimates yielded slopes
of −0.084 (intercept = 0.703, r = .916) for the walk–walk
estimate and −0.204 (intercept = 1.141, r = .991) for the walk–
throw estimate, indicating that encoding error based on walking was flatter than encoding error based on throwing (Fig. 5).
As we explained in the introduction to this experiment, the
extrinsic model predicts that no difference should emerge
between these two estimates of encoding error, whereas the
Atten Percept Psychophys (2014) 76:230–246
intrinsic model predicts that the estimate based on walking
should be smaller than the estimate based on throwing
(ÊNCww < ÊNCwt). Our results are consistent with this prediction, indicating that the overall reproduction error is smaller
with matching action modes. These findings suggest that
additional error, such as error due to different idiothetic information in different modalities, may be associated with a
mismatch between the outbound and response modes.
Self-reported difficulty ratings for the four conditions had
means of 2.63 (SD = 0.93) for walk–walk, 5.90 (SD = 1.25)
for walk–throw, 3.58 (SD = 1.14) for view–walk, and 5.23
(SD = 1.88) for view–throw. These ratings are in ordinal
agreement with the observed reproduction errors. Tukey
tests on the self-reported difficulty ratings showed that
walk–walk was judged as being significantly easier than
walk–throw (p < .001), but not easier than view–walk
(p = .188). View–walk was rated as being significantly
easier than view–throw (p < .01). Finally, participants did
not rate view–throw as being significantly easier than walk–
throw (p = .560). Thus, distance reproduction is judged to be
easiest when the outbound and response modes match.
The results of Experiment 1 indicate that distance reproduction is more accurate with matching outbound and response
modes, consistent with the intrinsic model. Yet performance
did not completely fall apart when the action mode changed
in the walk–throw condition, as one might expect for
mismatched idiothetic information. This observation suggests that participants may have established a rough calibration between the idiothetic information associated with
walking and that associated with throwing, perhaps on the
basis of previous experience walking to retrieve thrown
objects. However, such a calibration exhibits systematic
error, for throwing overshoots short walked intervals and
undershoots long walked intervals.
The results of Experiment 1 are in agreement with previous
research. Schwartz (1999) found that when step length and
walking speed differed on the outbound and response paths,
distance reproduction was compressed. Similarly, Mittelstaedt
and Mittelstaedt (2001) asked participants to reproduce distances of 2–21 m, using slow, standard, or fast walking speeds
on the outbound and response paths. When the outbound and
response speeds matched, distance reproduction was highly
accurate. However, when the walking speeds did not match,
the length of the response path depended on the difference
between the outbound and response speeds. Together, these
findings indicate that mismatches in step length, step frequency, or walking speed can reduce reproduction accuracy. Sun
et al. (2004) took these finding a step further, by comparing
visual estimates and walking estimates. They found that when
outbound and response modes matched, distance estimations
were more accurate than when they mismatched.
In sum, Experiment 1 contrasted the extrinsic and intrinsic
models of distance reproduction. The results suggest that
Atten Percept Psychophys (2014) 76:230–246
distance reproduction is more accurate when the outbound and
response modes match, even when taking into account differing accuracies in production. These results are in line with
previous literature finding that differences in gait type and
speed affect distance reproduction. Although these previous
findings hinted at the intrinsic model, none of them corrected
for production error. The present results provide direct evidence for the intrinsic model and against the extrinsic model.
In addition, our procedure offers a practical estimate of
encoding error that can be used in future work on path
integration.
241
Turvey et al. (2012) over a shorter distance range (2–8 m, as
opposed to 8–24 m).
The extrinsic model predicts that participants should be
able to encode objective distance whether walking or galloping, so distance reproduction should be equally accurate in all
four conditions. In contrast, the intrinsic model predicts that
participants should be less accurate in the gallop–walk and
walk–gallop conditions, when the outbound and response
modes differ, than in the walk–walk and gallop–gallop conditions, when the modes match. In Experiment 2a, we fully
crossed walking and galloping, whereas in Experiment 2b
we more closely examined the gallop–walk and walk–walk
conditions.
Experiment 2
Method
Whereas in Experiment 1 we attempted to analyze distance
reproduction into encoding error and production error, Experiment 2 directly tested whether distance reproduction depends
on the match between the outbound and response modes.
Specifically, we fully crossed the outbound and response
modes, in this case a walking gait and a bipedal “galloping”
gait, to ensure the proper control conditions.
Walking and galloping are qualitatively more similar than
the walking and throwing modes tested in Experiment 1. Both
gaits generate idiothetic information for locomotor displacement that is produced by stepping with the lower limbs, with a
double-support phase. However, in a gallop the participant
leads every stride with one leg and follows with a catch-up
step in the contralateral leg. Walking is a “primary” gait and
galloping a “secondary” gait, as classified by symmetry group
analysis of minimal neural pattern generators for bipedal and
quadrupedal gaits (Golubitsky et al., 1999; Pinto &
Golubitsky, 2006). Primary bipedal gaits are generated by
similar signals to both legs (two-legged hop, two-legged
jump) or by half-period phase shifts between them (walk,
run), whereas secondary bipedal gaits (skip, gallop) require
two types of signals. Turvey et al. (2009) hypothesized that
distance measurement is invariant over gaits within a symmetry class, but not across classes.
Turvey et al. (2009) found less accurate distance reproduction in a gallop–walk condition than in walk–walk and gallop–gallop conditions, consistent with the intrinsic model and
the gait symmetry hypothesis. However, they did not fully
cross the outbound and response modes with a walk–gallop
condition, so it was not clear whether undershooting in the
gallop–walk condition was due to a lack of transfer or
reflected a calibration between galloping and walking. While
the present article was in revision, Turvey et al. (2012) published a completely crossed experiment showing that participants in the walk–gallop condition reciprocally overshot relative to the gallop–gallop condition, suggesting a mutual
calibration. Experiment 2 thus constitutes a replication of
Participants A group of 19 participants took part in Experiment 2a (11 male, eight female; age 23.0 ±5.686 years, range
18–41); six additional participants failed to finish all experiment sessions and were not included in the analysis. The 20
participants in Experiment 1 also took part in Experiment 2b
(ten male, ten female; age 24.05 ±5.987 years, range 19–43).
They all had normal or corrected-to-normal vision and gave
informed consent to participate in the study, in accordance
with the Brown University Institutional Review Board.
Procedure The experimental setup was the same as in Experiment 1. In addition, in Experiment 2a, audio cues were
presented over a set of noise-canceling headphones, along
with white noise to reduce external noise.
In Experiment 2a, four conditions were presented: walk–
walk, gallop–gallop, walk–gallop, and gallop–walk. Four outbound distances were used in each of the four conditions: 2, 4,
6, and 8 m. Participants completed eight trials at each distance
in a random order, yielding 32 trials per condition, for a total
of 128 trials. Trials were blocked by condition, and the order
of the blocks was randomized for each participant. Participants completed all four blocks in two 1-h sessions, two
blocks per session, for a within-subjects design. At the end
of the second session, they filled out a brief questionnaire in
which they described any strategies they might have used, and
rated the difficulty of each of the tasks on a 1–7 scale.
In Experiment 2b, two conditions were presented: walk–
walk and gallop–walk. Five outbound distances were used in
the two conditions: 2, 4, 5, 6, and 8 m. Participants completed
ten trials at each distance in a random order, yielding 50 trials
per condition, for a total of 100 trials. Trials were blocked by
condition, and the order of the blocks was randomized for
each participant. Participants completed both blocks together
with Experiment 1, in three 1.5-h sessions, two blocks per
session, in a within-subjects design. At the end of the last
session, they filled out a brief questionnaire in which they
242
Atten Percept Psychophys (2014) 76:230–246
described any strategies that they might have used and rated
the difficulty of each of the tasks on a 1–7 scale.
The experimenter demonstrated the gallop step at the
beginning of the session, instructing participants that they
were to step forward with one foot and then bring the opposite
foot in line with the first. Participants were allowed to lead
with whichever foot they felt most comfortable and were
allowed to pause between steps, as long as they were consistent throughout the block of trials. Thus, we did not distinguish gaits that Turvey et al. (2009) described as a walking
gallop (with a pause in the double-support phase) and a
running gallop (without a pause), although most participants
used a running gallop. Otherwise, the procedure was the same
as that in the walk–walk condition of Experiment 1.
Occasional trials were excluded from the analysis when
the tracker lost the participant’s position, the mouse did not
record the data properly, or a participant lost his or her place.
These errors occurred on fewer than 4 % of the trials. The
analysis was performed on both the response distance (to
derive constant error) and the within-subjects standard deviation of response distance (variable error) in each condition.
Results and discussion
The results of Experiment 2a are represented in Fig. 6, which
plots mean response distance as a function of outbound
distance for the four conditions. Distance reproduction appears to be more accurate (closer to the diagonal) when the
outbound and response gaits match than when they differ. A
planned two-way repeated measures ANOVA on response
distance for the four conditions showed a main effect of
outbound distance [F(3, 54) = 344.474, p < .001], a main
effect of condition [F (3, 54) = 5.136, p < .01], and a significant interaction [F (9, 162) = 1.974, p < .05]. We also found
an overall effect of outbound distance on the within-subjects
standard deviation [F (3, 54) = 34.785, p < .001], but no effect
of condition [F(3, 54) = 2.113, p = .109) or interaction [F (9,
162) = 0.329, p = .964].
To compare particular conditions, we performed planned
comparisons using two-way repeated measures ANOVAs on
response distance. The first comparison, between the walk–
walk and gallop–gallop conditions, indicated that walking and
galloping were equally accurate in distance reproduction
(Fig. 6a): We observed a significant main effect of outbound
distance [F(3, 54) = 728.169, p < .001], but no main effect of
condition [F (1, 18) = 2.308, p = .146] and no interaction [F (3,
54) = 1.032, p = .386]. In addition, the within-subjects standard deviations for these conditions did not significantly differ
[F (1, 18) = 0.005, p = .942].
In contrast, significant differences emerged between
matching and mismatching gaits. A planned comparison of
the walk–walk and walk–gallop conditions revealed a
Fig. 6 Mean response distance as a function of outbound distance for the
four conditions in Experiment 2a. The solid gray diagonal lines indicate
accurate performance; error bars represent between-subjects standard
errors. a Walk–walk and gallop–gallop. b Walk–gallop and gallop–walk
significant effect of outbound distance [F(3, 54) = 497.390,
p < .001] and a significant effect of condition [F(1, 18) =
13.587, p < .01], but no Distance × Condition interaction
[F (3, 54) = 0.562, p = .642]. The planned comparison between the walk–walk and gallop–walk conditions revealed a
main effect of distance [F (3, 54) = 396.282, p < .001], but no
effect of condition [F (1, 18) = 1.024, p = .325] or interaction
[F (3, 54) = 2.064, p = .116]. The planned comparison between the gallop–gallop and walk–gallop conditions yielded a
main effect of distance [F(3, 54) = 682.563, p < .001], a main
effect of condition [F (1, 18) = 4.633, p < .05], and no
Distance × Condition interaction [F (3, 54) = 0.940, p =
.428]. The comparison between the gallop–gallop and gallop–walk conditions yielded a main effect of distance [F (3,
54) = 564.724, p < .001], a marginal effect of condition [F (1,
Atten Percept Psychophys (2014) 76:230–246
18) = 3.487, p = .078], and a significant interaction [F(3, 54)
= 3.494, p < .05]. Taken together, these results indicate that
performance with mismatched gaits differs from that with
matched gaits, showing either a compressed response range
or lower response distances.
The final comparison, between the walk–gallop and gallop–walk conditions (Fig. 6b), yielded a main effect of distance [F (3, 54) = 500.018, p < .001], a main effect of condition [F(1, 18) = 7.416, p < .05], and a significant interaction
[F (3, 54) = 3.605, p < .05]. This finding demonstrates that
gallop–walk systematically undershot relative to walk–gallop.
Linear regressions yielded slopes of 0.823 (intercept =
0.771, r = .999) for the walk–walk condition, 0.855 (intercept
= 0.827, r = .998) for the gallop–gallop condition, 0.866
(intercept = 1.024, r = .998) for the walk–gallop condition,
and 0.747 (intercept = 0.998, r = .999) for the gallop–walk
condition. These results confirm that the gallop–walk condition exhibited the greatest response compression. The smallest
response compression occurred in the walk–gallop condition,
which also had the highest intercept, indicating a general
overshoot in that condition.
Considering the results in terms of the accuracy of distance
reproduction, the mean absolute (unsigned) errors for the four
conditions were walk–walk (M = 0.616 m, SD = 0.232),
gallop–gallop (M = 0.638 m, SD = 0.105), gallop–walk (M
= 0.854 m, SD = 0.334), and walk–gallop (M = 0.731 m, SD
= 0.069). A two-way repeated measures ANOVA on absolute
errors showed an effect of outbound distance [F (3, 54) =
4.550, p < .01], a marginal effect of condition [F(3, 54) =
2.552, p = .065], and a marginal Distance × Condition interaction [F(9, 162) = 1.905, p = .055]. Post-hoc comparisons
between the conditions revealed that the walk–walk condition
had significantly lower absolute errors than did the gallop–
walk condition (p < .05). This finding suggests that conditions
in which the outbound and response modes matched had
lower errors than did conditions in which they did not match,
supporting the intrinsic model.
Finally, ratings of task difficulty showed an overall effect of
condition [F(3, 54) = 30.150, p < .001]. Post-hoc Tukey tests
revealed that the walk–walk condition (M = 2.45, SD = 1.07)
was rated as being significantly easier than both the walk–
gallop (M = 4.74, SD = 1.24, Tukey test, p < .001) and the
gallop–walk (M = 4.84, SD = 1.21, Tukey test, p < .001)
conditions, but was not different from the gallop–gallop task
(M = 3.05, SD = 1.62, Tukey test, p = .482). Likewise, the
gallop–gallop condition was rated as being easier than both
the walk–gallop (Tukey test, p = .001) and the gallop–walk
(Tukey test, p < .001) conditions, which were not different
from each other (Tukey test, p = .994).
Experiment 2b pursued the contrast between the gallop–
walk and walk–walk conditions in more detail (Fig. 7). Distance reproduction in the walk–walk condition appeared to be
more accurate (closer to the diagonal), whereas gallop–walk
243
Fig. 7 Mean response distance as a function of outbound distance for the
two conditions in Experiment 2b. The diagonal line indicates accurate
performance; error bars represent between-subjects standard errors
exhibited more undershooting at larger distances. A two-way
repeated measures ANOVA on response distance showed a
main effect of outbound distance [F(4, 76) = 619.409, p <
.001] and a significant Distance × Condition interaction [F (4,
76) = 6.041, p < .001], indicating greater response compression in the gallop–walk condition. An analysis of the withinsubjects standard deviations revealed only a main effect of
distance [F (4, 76) = 35.554, p < .001], with no interaction.
Thus, distance reproduction appears to be more accurate when
the outbound and response modes match.
Linear regressions on the mean response distance yielded
slopes of 0.892 (intercept = 0.411, r = .999) for the walk–walk
condition and 0.777 (intercept = 0.734, r = .997) for the
gallop–walk condition (Fig. 7), confirming greater response
compression in gallop–walk. The mean absolute error for
walk–walk was 0.611 m (SD = 0.206), whereas for gallop–
walk the mean absolute error was 0.891 m (SD = 0.313). A
two-way repeated measures ANOVA on the absolute errors
yielded a significant effect of outbound distance [F(4, 76) =
12.029, p < .001] and a significant effect of condition [F (1,
19) = 6.732, p < .05]. This result indicates that the matched
condition was more accurate than the mismatched condition.
Similarly, the gallop–walk condition (M = 4.20, SD = 1.40)
was rated as being significantly more difficult than the walk–
walk condition (M = 2.63, SD = 0.93, Tukey test, p < .01),
such that distance reproduction was found to be easier with
matching outbound and response modes.
The results of Experiment 2 are consistent with the intrinsic
model for distance reproduction, as performance was more
accurate when the action mode was the same on the outbound
and response paths. In contrast to Experiment 1, both the
outbound and response modes generated proprioceptive information from the legs and vestibular information for selfmotion, so the mismatch between walking and galloping
244
was limited to the details of these gait patterns. Nevertheless,
the differences in idiothetic variables were sufficient to induce
significant differences in distance reproduction.
The consistent pattern of overshooting in the walk–gallop condition and undershooting in the gallop–walk condition offers an important clue to the path integration process.
First, it shows that these two gaits are systematically related, but are not accurately calibrated to each other. The
extrinsic model holds that different gaits encode objective
distance, and hence they should be accurately calibrated,
yet they are not. A possible explanation is that distance
reproduction is simply poor in the unfamiliar galloping gait.
But Experiment 2a showed that gallop–gallop is as accurate
as walk–walk, indicating that galloping reproduces distance
quite well. Thus, the finding that the gaits were not wellcalibrated to each other implies that they do not encode
objective distance. Second, the over- and undershooting
suggests that walking and galloping are mutually calibrated, but inaccurately so, presumably due to limited prior
experience. Specifically, the slope ratio of gallop–walk
(0.747) to walk–gallop (0.866) yields a scaling constant of
0.863 between walking and galloping, such that walking
undershoots a previously galloped distance, and galloping
overshoots a previously walked distance. The findings of
Experiment 2 can thus be explained by the intrinsic model:
Matched idiothetic information on the outbound and response paths allows for accurate distance reproduction,
whereas mismatched information yields systematic overand undershooting.
Our results replicate those of Turvey et al. (2012) over a
shorter distance range. They likewise found that distance
reproduction was significantly less accurate in the gallop–
walk and walk–gallop conditions than in the walk–walk and
gallop–gallop conditions, and that the latter conditions did not
differ from each other. Moreover, their gallop–walk condition
also undershot the corresponding matched-gait condition,
whereas the walk–gallop condition overshot it. This pattern
of results is consistent with both the intrinsic model and the
gait symmetry hypothesis, which will be revisited in the
General Discussion.
We interpret the results of Experiment 2 to be contrary to
the extrinsic model but supportive of the intrinsic model.
Distance reproduction depends on the match between the
outbound and response modes; specifically, performance is
more accurate when the outbound and response gaits are the
same, relative to when they differ.
General discussion
The present results offer converging evidence of an intrinsic,
action-scaled metric for the human odometer. These two experiments showed that distance reproduction is significantly
Atten Percept Psychophys (2014) 76:230–246
more accurate when the outbound action mode matches the
response action mode. In Experiment 1, we held the outbound
mode constant (walk) and varied the response mode (walk or
throw). We found that reproduction error was significantly
larger in the walk–throw than the walk–walk condition, even
after correcting for production accuracy (view–walk and
view–throw conditions). Equivalently, we found that the estimated encoding error of outbound walking was significantly
smaller in the walk–walk than in the walk–throw condition.
Thus, overall distance reproduction was more accurate when
the outbound and response modes matched.
This finding is inconsistent with the extrinsic model, which
assumes that objective distance is encoded on the outbound
path and reproduced during the response. On the other hand, it
is consistent with the intrinsic model, which holds that actionscaled information on the outbound path is matched on the
response path, within an action mode. When the outbound and
response modes differ, distance reproduction is less accurate,
but does not fail completely. We suggest that different action
modes may become approximately calibrated to each other if
they are used to traverse the same locations.
In Experiment 2, we crossed the outbound mode with the
response mode (walk or gallop). Distance reproduction was
again more accurate when the action modes matched than
when they did not. This effect is unexpected on the view
that objective distance is encoded and reproduced in both
gaits, but it is consistent with the matching of action-scaled
information that is specific to each gait. In particular, the
finding that the gallop–walk condition consistently undershot the walk–gallop condition cannot be explained by the
notion that each gait encodes objective distance. Rather, it
appears that walking and galloping are mutually calibrated,
but with a proportional scaling.
Turvey et al. (2009; Turvey et al., 2012) proposed that the
measurement of distance by locomotion is specific to a gait
symmetry class. Bipedal gaits have two symmetry classes:
primary gaits, which are characterized by reflectional symmetry, and secondary gaits, which are only characterized by
rotational symmetry. Turvey et al. (2009) reported that reproduction accuracy was high even with unmatched outbound
and response gaits, as long as they both came from the same
symmetry class, including the primary gaits run–walk and
backward walk–walk, and the secondary gaits running gallop–walking gallop. Nonetheless, Turvey et al. (2009)
maintained that the human odometer measures objective traversed distance.
We believe that these results support the intrinsic model.
Turvey et al.’s (2009) conclusion that distance measurement is
gait-symmetry-specific implies that each gait class possesses
its own yardstick, consistent with the intrinsic hypothesis.
However, gait symmetry classes offer only a first approximation of the relevant action modes. On the one hand, accurate
distance reproduction across different gaits within a symmetry
Atten Percept Psychophys (2014) 76:230–246
class may be attributable to similarities in idiothetic variables.
For example, within the secondary gaits, it seems likely that
idiothetic information in a backward walk is quite similar to
that in a walk, and a running gallop is quite similar to a
walking gallop (the former merely eliminates a pause during
double-support). On the other hand, action modes appear to be
more fine-grained than symmetry classes. Contrary to the
symmetry hypothesis, a change in step length or speed between the outbound and response paths interferes with distance reproduction in walking (Mittelstaedt & Mittelstaedt,
2001; Schwartz, 1999), despite the fact that the gait class
remains the same. Action modes would seem to have a basis
in common idiothetic information, rather than in gait symmetry classes per se.
We contend that action modes are individuated by the
family of actions over which distance reproduction is invariant, and that each family shares a common complex of
idiothetic variables related to locomotor displacement. Two
cases, in which distance reproduction is accurate despite different outbound and response gaits, appear to present a challenge to the intrinsic hypothesis. Schwartz (1999) reported
that distance reproduction was equal in jog–walk and walk–
walk conditions, and Turvey et al. (2009) reported the same in
run–walk and walk–walk conditions. Walking, jogging, and
running are all primary gaits, and they seem to generate
different patterns of idiothetic information. However, the finding that distance reproduction is invariant over this family of
gaits leads us to expect that they could share a common
higher-order complex of idiothetic variables.
Hence, both the intrinsic model and the gait symmetry
hypothesis imply that the metric for human odometry is an
action-scaled quantity based on idiothetic information, not an
extrinsic measure of objective distance. The notion that each
action mode or symmetry class has its own “yardstick” for
distance would seem to be problematic for path integration,
for any shift in action mode during the course of travel would
yield homing errors. On the other hand, an intrinsic metric
avoids the difficulties of converting idiothetic variables to
objective distances: As long as the navigator remains in one
action mode during the journey, homing performance will be
reasonably accurate and robust. For example, in a triangle
completion task, idiothetic variables that underestimate objective distance would yield an “intrinsic path” that was larger
than, but similar to, the triangle for the “extrinsic path,” and
thus would successfully return to the home location. This
similar-path argument also applies to more complex outbound
routes. However, the argument does not hold for rotation: An
intrinsic metric that misestimated objective turn angles would
yield systematic homing errors. We will investigate this question in a subsequent study.
In sum, we have found that distance reproduction does not
depend on encoding objective distance, but on an actionscaled measure of locomotor displacement. The human
245
odometer thus appears to possess an intrinsic, rather than an
extrinsic, metric: Distance is “measured by the body” using
idiothetic information. This solution is sufficient to support
successful path integration within an action mode, while
avoiding the difficulties of measuring objective distance.
Author note Preparation of this article was supported by National
Science Foundation awards BCS-0214383 and BCS-0843940. The authors also thank Henry Harrison, Joost de Nijs, Mintao Zhao, Michael
Fitzgerald, and the members of the VENLab for assistance with the
research.
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