1
1
1,2
1
2
Dynamic touch is the sense used to detect meaningful properties of objects through wielding and hefting (Gibson, 1966). Evidence suggests that the eigenvalues (I k
) of the inertia tensor support the perception of object properties during dynamic touching
(Turvey & Carello, 1995).
Fitzpatrick, Carello, and Turvey
(1994) found, for objects of different shapes and densities, that perceived extent is a function of I in Figure 1.
1 and I
3
I
1
around the diagramed axis is quantified by the largest eigenvalue of the inertia tensor or I
1
.
(Bottom) Resistance to rotation around the diagramed axis is quantified by the smallest eigenvalue of the inertia tensor or I
3
.
I
3
Jacobs and Michaels (in press) have suggested that perceivers change in the variables that they exploit during learning. According to their theory of “direct learning”, the learning process is characterized as movement across a low-dimensional information manifold toward a locus that allows for better performance (see Figure 2).
We first asked whether learning occurred. A paired t-test comparing the correlations of length judgments with the feedback variable showed improvement from the pre-test (r av
= .79) to the posttest (r av
= .92) was significant, t(9) = 5.44, p < .001.
The usefulness function of the two dimensional informational manifold was computed.
We then asked how learners moved across that space. For each participant, we determined the occupied locus on the information manifold for each block of trials by finding which locus correlated most highly with judgments. To determine whether learning followed the path predicted by the usefulness function of the space, we plotted the observed learning path on the manifold for each participant. The plots of four participants are overlaid in Figure 8 (a and b). As is clear from the figure, learning (the change in locus) proceeds toward the optimum.
A.
B.
1
0
information space (in red). Loci on the horizontal information line differ in their usefulness (0 is useless, 1 is propertyspecifying) for detecting a particular environmental property.
The green vertical dashed line indicates the locus that is maximally useful for detecting a given property. The vector arrows (in blue) illustrate that expected movement along the line (during learning) follows from the usefulness function.
The first experiment explicitly designed to test direct learning used the dynamic touch paradigm
(Arzamarski, Isenhower, Jacobs, & Michaels,
2007). As predicted, when given appropriate feedback, participants moved across the space toward the most useful locus in the space. In the tested case, the information space was one dimensional, capturing relations between I
1 and
3
, as shown in Figure 3.
1/I
3
I
1 a /I
3 b
I
1
I
1 a I
3 b
I
3
used in Arzamarski et al. (2007). I and I
3 were used as coordinate
1 dimensions in the information space.
These variables collapse onto a 1dimensional information line.
Chan (1995) suggested that grasped diameter is an important variable for length perception (see Figure 4).
Is grasped diameter a useable coordinate dimension in the information-space for length perception by dynamic touch?
d
0
/I
3 d
0 d
0
I
3
0
role of grasped diameter in length perception. Grasped diameter of handheld rods was varied while I
3 was kept constant. Rods with larger grasped diameters were perceived to be shorter.
1/I
3 d
0 a I
I
1 a
1 b /I
3
/d
0 b I
3 c c
I
1 d
0 a I
1 b I
3 c
I
1 a I
3 b /d
0 c
I
3
Given feedback based on I
1
, I
3
, and the outer diameter of the objects (d
0
) using the
Arzamarski et al. (2007) paradigm, can participants be compelled to use d
0
?
Can a two-dimensional information space (see
Figure 5) capture the learning process during the task?
1/d
0
I
3
1/d
0
I
3
/d
0
A two-dimensional information manifold used in the current study. I
1
, I
3
, and d o coordinate dimensions.
variables collapse onto a 2dimensional information plane.
are
These
usefulness for each locus (0 is useless; 1.0 is L value of (–1, 0) represents 1/d
0 and (1, 0), d
0 f
-specifying). The origin (0, 0) represents use of I
. Locus (0, -1) is 1/I
3 and (0, 1) is I
3
1
. A
. Intermediate values populate the intermediate points. (B) A closer view of the red boxed region. Each mark represents a block of trials for a participant (circles mark the first block). Lines connecting blocks show movement along the manifold.
To test whether, over participants, there was an increase in reliance on d variables, we subjected the zero-order correlations between judgments and I
1
0
0 to a repeated measures ANOVA and found a significant interaction between variable and block, F(6, 72) = 2.58, p < .05 (see Figure 9).
, I
3 related
, and d
1
between participants’ judgments and variables I
1
, I
3 for each block of
, and d
0 trials.
After feedback, participants’ reliant variables.
on I
3 judgments became more reliant on d
0 related variables and less related
0.8
0.6
Pearson R
Correlations
0.4
0.2
0
-0.2
-0.4
J-I1
J-I3
J-d0
Pretest Feedback 1 Feedback 2 Posttest
Block
We conclude that participants shifted their attention to an informational variable on this new two-dimensional informational manifold. Grasped diameter appears to be a useful coordinate dimension in the information space for length perception.
It is important to note that due to the high intercorrelations among variables, these findings should be validated with other collections of stimuli in which the inertial moments and diameters are related differently.
Future research will be aimed at validating the information space and identifying the convergence information that guides learning. In addition to running a no-feedback control condition, we hope to demonstrate that not every variable one might suppose
(e.g., texture and thermal conduction) matters to the perception of length in dynamic touch. If the informational space is high-dimensional, there is not sufficient constraint on what informational variables possibly need to be attended to.
Ten right-handed students at the University of Connecticut made length judgments using the apparatus depicted in Figure 6. The experiment consisted of four randomized blocks: a pretest, two training blocks, and a posttest, each with the 38 objects (see Figure 7). In the pretest and posttest, participants received no feedback on their length judgments. During training blocks, participants received feedback; the experimenter moved the indicator to a feedback length, L f
, corresponding to a specific locus on the 2-dimensional manifold. L f
1
, I
3
, and d o was a function of
(see Equation 1) so as to reduce the intercorrelations among variables.
L f
= (0.5*e (-0.5*ln(do))+(0.25*ln(I1))+(0.2*ln(I3)) ) (1)
The research reported here was supported by the National Science Foundation under Grant No. BCS
0339031, and while Claire F. Michaels was serving at the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
from view, and they wore a glove to eliminate information from thermal conduction or texture.
Participants made length judgments by moving an indicator to the perceived distal end of the object.
and rods of various lengths, diameters, and materials
(wood, PVC, and metal), constituted the stimulus set.
Arzamarski, R., Isenhower, R. W., Jacobs, D. M., & Michaels, C. F. (2007). Direct learning
Chan, T-C. (1995). The effect of density and diameter on haptic perception of rod length.
Fitzpatrick, P., Carello, C., & Turvey, M. T. (1994). Eigenvalues of the inertia tensor and exteroception by the “muscle sense.” Neuroscience, 60, 551-568.
Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton
Mifflin.
Jacobs, D. M., & Michaels, C. F. (in press). Direct Learning. Ecological Psychology.
Turvey, M.T., & Carello, C. C. (1995). Dynamic touch. In W. Epstein & Rogers (Eds.),
490) New York: Academic Press.