INTRODUCTION

1. 1/I3 I1 I3 I3 I1a/I3b I1aI3b 1 I1 0 d0 d0aI1b/I3c d0aI1bI3c 1/I3 I3 I1 I1a/d0bI3c I1aI3b/d0c 1/d0 d0/I3 d0I3 1/d0I3 I3/d0 d0 Grasped Diameter and the Information Space for Haptic Length Perception Robert W. Isenhower1, Ryan Arzamarski1, and Claire F. Michaels1,2 1Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs, CT, U.S.A. 2National Science Foundation INTRODUCTION RESULTS Dynamic Touch 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 (rav = .79) to the posttest (rav = .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. Dynamic touch is the sense used to detect meaningful properties of objects through wielding and hefting (Gibson, 1966). Evidence suggests that the eigenvalues (Ik) of the inertia tensor support the perception of object properties during dynamic touching (Turvey & Carello, 1995). Figure 1. (Top) Resistance to rotation around the diagramed axis is quantified by the largest eigenvalue of the inertia tensor or I1. (Bottom) Resistance to rotation around the diagramed axis is quantified by the smallest eigenvalue of the inertia tensor or I3. Fitzpatrick, Carello, and Turvey (1994) found, for objects of different shapes and densities, that perceived extent is a function of I1and I3,as shown in Figure 1. Direct Learning A. B. 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). Figure 2. A. The usefulness function of a 1-dimensional information space (in red). Loci on the horizontal information line differ in their usefulness (0 is useless, 1 is property-specifying) 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. Figure 8. (A) The usefulness function for the information manifold. The vertical axis represents usefulness for each locus (0 is useless; 1.0 is Lf-specifying). The origin (0, 0) represents use of I1. A value of (–1, 0) represents 1/d0 and (1, 0), d0. Locus (0, -1) is 1/I3 and (0, 1) is I3. 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. 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 I1and I3, as shown in Figure 3. To test whether, over participants, there was an increase in reliance on d0related variables, we subjected the zero-order correlations between judgments and I1, I3, and d0 to a repeated measures ANOVA and found a significant interaction between variable and block, F(6, 72) = 2.58, p < .05 (see Figure 9). Figure 3. The information manifold used in Arzamarski et al. (2007). I1 and I3 were used as coordinate dimensions in the information space. These variables collapse onto a 1-dimensional information line. Figure 9. The correlations between participants’ judg-ments and variables I1, I3, and d0 for each block of trials. After feedback, participants’ judgments became more reliant on d0 related variables and less reliant on I3 related variables. Research Questions 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? Figure 4. Chan (1995) examined the role of grasped diameter in length perception. Grasped diameter of hand-held rods was varied while I3 was kept constant. Rods with larger grasped diameters were perceived to be shorter. CONCLUSIONS 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. Given feedback based on I1, I3, and the outer diameter of the objects (d0) using the Arzamarski et al. (2007) paradigm, can participants be compelled to use d0? Can a two-dimensional information space (see Figure 5) capture the learning process during the task? Figure 5. A two-dimensional information manifold used in the current study. I1, I3, and do are coordinate dimensions. These variables collapse onto a 2-dimensional information plane. METHOD 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, Lf, corresponding to a specific locus on the 2-dimensional manifold. Lf was a function of I1, I3, and do (see Equation 1) so as to reduce the intercorrelations among variables. Lf = (0.5*e(-0.5*ln(do))+(0.25*ln(I1))+(0.2*ln(I3))) (1) ACKNOWLEDGMENTS 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. REFERENCES Arzamarski, R., Isenhower, R. W., Jacobs, D. M., & Michaels, C. F. (2007). Direct learning in dynamic touch. Under review. Chan, T-C. (1995). The effect of density and diameter on haptic perception of rod length. Perception & Psychophysics, 57, 778-786. 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.), Handbook of perception and cognition: Perception of space and motion (pp. 401- 490) New York: Academic Press. Figure 6. Participants’ right arms were occluded 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. Figure 7. Thirty-eight pipes and rods of various lengths, diameters, and materials (wood, PVC, and metal), constituted the stimulus set.