Perceiving the lengths of rods wielded in differentmedia

In two experiments, we investigated the ability of participants to report the lengths of rods wielded in air or water. Homogeneous aluminum rods were employed in Experiment 1. The inertia of the rods was manipulated in Experiment 2 through the use of attached masses. Although the torques required in order to wield rods in water are substantially greater than those required to wield rods in air, the perceived lengths of rods wielded in the two media were very similar. Perceived length was found to be a function primarily of inertia in both media. The experiments also revealed a small influence of resistance due to the denser medium of water. The results demonstrate the ability of perceivers to extract a physical invariant from a complex array of forces. The discussion is focused on the role of invariants in dynamic touch.     

The effect of density and diameter on haptic perception of rod length

Three experiments on the effect of density and diameter on haptic perception of rod length are reported. In Experiment 1, the subjects wielded visually occluded rods of different densities. Perceived length was found to be affected by the density of the rod regardless of the actual length. In Experiment 2, three aluminum rods of different lengths with handles of four different diameters were wielded. Perceived length of the rod was found to be shorter as the diameter of the handle with which it was wielded increased. A diameter—length illusion was thereby produced. In Experiment 3, visually occluded rods of different diameters but of the same moment of inertia about thex-axis were wielded with the right hand, and tubes of different diameters were felt with the left hand. The subjects were instructed that their right hand was grasping a handle, and that the actual diameter of the rod could be felt with the left hand. Rods were perceived to be shorter if a larger diameter was felt with the left hand. The results showed that perceived length is not just a function of actual rod length, and that it is not accounted for by inertia only. The results are further discussed in terms of the nature of invariants and the effect of knowledge on perception.     

Haptically perceiving the distances reachable with hand-held objects

Nine experiments are reported on the ability of people to perceive the distances reachable with hand-held rods that they could wield by movements about the wrist but not see. An observed linear relation between perceived and actual reaching distances with the rods held at one end was found to be unaffected by the density of the rods, the direction relative to the body in which they were wielded, and the frequency at which they were wielded. Manipulating (a) the position of an attached weight on an otherwise uniformly dense rod and (b) where a rod was grasped revealed that perceived reaching distance was governed by the principal moment(s) of inertia (I) of the hand-rod system about the axis of rotation. This dependency on moment of inertia (I) was found to hold even when the reaching distance was limited to the length of rod extending beyond an intermediate grasp. An account is given of the haptic subsystem (hand-muscles-joints-nerves) as a smart perceptual instrument in the Runeson (1977) sense, characterizable by an operator equation in which one operator functionally diagonalizes the inertia and strain tensors. Attunement to the invariants of the inertia tensor over major physical transformations may be the defining property of the haptic subsystem. This property is discussed from the Gibsonian (ecological) perspectives of information as invariants over transformations and of intentions as extraordinary constraints on natural law.     

Haptic perception of partial-rod lengths with the rod held stationary or wielded

Three experiments on the haptic perception of partial-rod lengths are reported. The rods were gripped between the two ends and held horizontal. The subjects held the rods stationary; the distribution of mass of the segment in front of the hand was fixed, while the distribution of mass of the segment behind the hand was varied. Perceived forward length was found to be significantly affected by the distribution of mass of the backward segment. Similar results were obtained when the rods were wielded. The results indicated that partial-rod lengths are specified by functions of mechanical perturbations acting on the hand, and not ay the breaking up of the first moment of mass or the moment of inertia of the rod by attention as suggested previously by others. The results are also discussed with respect to invariant detection and attention.     

Perception of the length of an object through dynamic touch is invariant across changes in the medium

Rotational inertia—a mechanical quantity that describes the differential resistance of an object to angular acceleration in different directions—has been shown to support perception of the properties of that object through dynamic touch (wielding). The goal of the present study was to examine if perception of the length of an object through dynamic touch depends on its rotational inertia, independent of the medium in which it is wielded. The participants (n = 14) wielded 12 different objects held in air or completely immersed in water and reported perceived lengths of those objects. Each object consisted of a rod of a particular density with a particular number of stacked steel rings attached at a particular location along its length. Perceived length was invariant across medium. In addition, a single-valued function of the major eigenvalue, I ₁, and the minor eigenvalue, I ₃, of the rotational inertia, I, of the 12 objects predicted the perceived lengths of those objects in both air and water, and the perceived lengths were invariant across the two media. These results support the hypothesis that the informational support for perception of the length of an object through dynamic touch is invariant across changes in the medium.     

Can shape be perceived by dynamic touch?

The possibility that some aspects of the shapes of solid objects can be perceived through dynamic touch, even when the objects are not touched, but simply wielded with a handle, was investigated in four experiments. Wooden solids were constructed of three sizes and five shapes: hemisphere, cylinder, parallelepiped, cone, and pyramid. Experiments 1 and 2 involved comparisons (judgments of same or different) between and among wielded objects of the same mass. In Experiments 3 and 4, subjects were required to wield an object and to select a match from a visible arrangement of objects of the five shapes; the wielded objects were of two sizes, each different from that of the visible objects. The success of subjects at these tasks, and the patternings of errors, are seen to involve the characteristic moment of inertia profiles of each shape, and a ratio of the object's resistances to rotation around orthogonal axes is shown to be a strong predictor of performance in the identification experiments. The results are discussed with reference to dynamic touch and to the notion of shape invariants that do not reduce to aspects of object surface.     

Inertia tensor and weight-percept models of length perception by static holding

S. J. Lederman, S. R. Ganeshan, and R. E. Ellis (1996) reported an experiment demonstrating that for occluded rods of equal mass and length but different diameters length perception by static holding was larger for rods of smaller diameter. They concluded that participants inferred length from illusory weight percepts. However, rods of equal mass and length that differ in diameter also differ in the eigenvalues of their respective inertia tensors. In the present experiments, the authors manipulated the diameters (Experiment 1) and the inertial eigenvalues (Experiments 4 and 5) of statically held objects. As has been shown with wielded objects, perceived length was a function of the eigenvalues. Additional experiments failed to confirm the expectation from the weight-percept model that perceived length maps to the estimated weight (Experiments 2 and 3). Physical quantities, not psychological quantities, seem to explain length perception by static holding.     

Haptically Perceiving the Length of One Rod by Means of Another

Two experiments examined perception of the extent of a target rod that is contacted and wielded by a second probe rod. The equations that define the dynamics of the probe-target system suggest a higher order moment of inertia as the relevant perceptual variable. The particular inertial term implicates parameters of both the target and probe rod. Experiment 1 manipulated the inertia of the target rod and Experiment 2 manipulated the inertia of the probe rod. In both experiments, perceived length was a function of the complex inertial term. Results were discussed in terms of haptic perception at a distance, the equivalence of inert and neural appendages, and the scaling of perceived to actual variables.     

The situational effects on haptic perception of rod length

Three experiments were conducted to investigate situational effects (manipulation, range, and prior experience) on the haptic perception of rod length. Each rod was held between its two ends with one hand. In Experiment 1, 32 participants judged length of rods using different manipulations. Perceived lengths were found to be dependent on manner of manipulation and not necessarily equal to actual lengths. Different parameters were detected in different manipulations. In Experiment 2, 8 participants judged rod lengths by wielding rods of two ranges: long and short. Perceived length was found to be affected by the range of rods evaluated successively in a single set. In Experiment 3, 9 participants judged rod lengths after an experience of handling dense or light rods. Perceived length was found to be affected by prior experience. Results are discussed in terms of how rod lengths can be perceived accurately by haptic modality without involving direct perception.     

Changing grasp position on a wielded object provides self-training for the perception of length

Calibration of perception to environmental properties typically requires experiences in addition to the perceptual task, such as feedback about performance. Recently, it has been shown that such experiences need not come from an external source or from a different perceptual modality. Rather, in some cases, a given perceptual modality can train itself. In this study, we sought to expand on the range of experiences in which this can occur for perception of the length of a wielded occluded object. Specifically, in two experiments, we investigated whether the act of perceiving the length of a wielded object from a given grasp position could recalibrate the perception of length from a different grasp position. In both experiments, three groups of participants perceived the lengths of wielded rods in a pretest, practice, and a posttest. The practice included either (a) experimenter feedback, (b) changing the grasp position on the object (and again attempting to perceive length), or (c) no additional experiences. In Experiment 1, participants changed their grasp position from the middle to the end of each rod, and in Experiment 2, they did so from the end to the middle of each rod. In both experiments, the results showed that perceiving length from a different grasp position can recalibrate (i.e., provide self-training for) the perception of length.     

Perceiving by Dynamic Touch the Distances Reachable With Irregular Objects

Observers wielded occluded objects and reported the distances reachable with the distal tips of the objects. Each object consisted of a cylindrical stem with two branches attached perpendicularly along its length; stem and branch lengths varied across objects. In Experiment 1, the branches were 180 deg. apart, both attached halfway along the stem. In Experiment 2, the branches were 180 deg. apart, one at one fourth and the other at three fourths of the stem length. In Experiment 3, the branches were 90 deg. apart, one at one fourth and the other at three fourths of the stem length. Observers had no foreknowledge of the objects' shapes. In each experiment, perceived reachable distance was found to be dependent on the maximum eigenvalue of the object's inertia tensor computed about the point of rotation in the wrist. Discussion focused on (a) quantifying shape for dynamic touch through the inertia ellipsoid, (b) the significance of the inertia tensor to the spatial abilities of dynamic touch, and (c) contrasting bases for theories of space perception (Lotze vs. Gibson).     

Berkeleian Principles in Ecological Realism: An Ontological Analysis

Three experiments are reported, which examined the relation between the percep- tion of the distance reachable with a hand-held rod that can be wielded but not seen and the rod's resistance to having its rotational speed changed by application of a torque. In these experiments, subjects wielded any given rod about an axis intermediate between its endpoints. The subject's task was to adjust a visible, movable surface to coincide with where he or she could reach with the given rod if allowed to hold it at its proximal end. Two experiments considered the effects of wielding a rod at different orientations to the pull of gravity. Rods were wielded either within a plane roughly perpendicular to the ground or within a plane roughly parallel to the ground. Plane of wielding did not affect the patterning of perceived reachable distances as a function of the various conditions, which included variations in the positioning of grasp and the positioning of a mass affixed to the rods. The patterning of the moments of inertia associated with the various conditions determined the patterning of perceived reachable distances. The third experiment restricted wielding to a plane roughly parallel to the ground and varied how the rods were grasped, either overhand or underhand. The variation in grasp amounted to a variation in the neuromuscular patterning associated with the wielding of any given rod. Perceived reachable distances proved to be indifferent to the overhand versus underhand contrast.     

Perceiving extents of rods by wielding: haptic diagonalization and decomposition of the inertia tensor

We report two experiments on the length-perception capabilities of the hand-related haptic subsystem. On each trial, a visually occluded rod was wielded by the subject at a position intermediate between its two ends. The position was either 1/2 or 3/4 of the rod's length. On two-thirds of the trials, a weight was attached to the rod at a point either above or below its center of gravity and not coincident with the hand's position. In Experiment 1, the subject's task was to perceive the distance reachable with the portion of the rod extending beyond the position of the grasp. In the second experiment, the subject's task was to perceive the distance reachable with the entire rod if it were held at its proximal end. In Experiment 1, perceived reaching distance was a function of the moment of inertia of the amount of rod forward of the grasp about an axis through the proximal end of the rod segment. In Experiment 2, perceived reaching distance was a function of the moment of inertia of the entire rod about the given axis of rotation intermediate between the rod's ends. The results are discussed in terms of (a) the notion of smart perceptual instruments capitalizing on invariant properties of the inertia tensor and (b) how the haptic decomposition of moments of inertia follows the principle of equivalence of forces.     

Metamers in the haptic perception of heaviness and moveableness

It is hypothesized that heaviness perception for a freely wielded nonvisible object can be mapped to a point in a three-dimensional heaviness space. The three dimensions are mass, the volume of the inertia ellipsoid, and the symmetry of the inertia ellipsoid. Within this space, particular combinations yield heaviness metamers (objects of different mass that feel equally heavy), whereas other combinations yield analogues to the size-weight illusion (objects of the same mass that feel unequally heavy). Evidence for the two types of combinations was provided by experiments in which participants wielded occluded hand-held objects and estimated the heaviness of the objects relative to a standard. Further experiments with similar procedures showed that metamers of heaviness were metamers of moveableness but not metamers of length. A promising conjecture is that the haptic perceptual system maps the combination of an object's inertia for translation and inertia for rotation to a perception of the object's maneuverability.     

The role of feedback information for calibration and attunement in perceiving length by dynamic touch

Two processes have been hypothesized to underlie improvement in perception: attunement and calibration. These processes were examined in a dynamic touch paradigm in which participants were asked to report the lengths of unseen, wielded rods differing in length, diameter, and material. Two experiments addressed whether feedback informs about the need for reattunement and recalibration. Feedback indicating actual length induced both recalibration and reattunement. Recalibration did not occur when feedback indicated only whether 2 rods were of the same length or of different lengths. Such feedback, however, did induce reattunement. These results suggest that attunement and calibration are dissociable processes and that feedback informs which is needed. The observed change in variable use has implications also for research on what mechanical variables underlie length perception by dynamic touch.     

Role of the inertia tensor in perceiving object orientation by dynamic touch.

Ss wielded an occluded L-shaped rod and attempted to perceive the direction in which the rod was pointing with respect to the hand. The pattern of the rod's different resistances to rotation in different directions, quantified by the inertia tensor, changes systematically with the rod's orientation. Perception of orientation by wielding is possible if the tissue deformation consequences of the rod's inertia tensor are detectable. It was shown that perceived orientation was a linear function of actual orientation for both free and restricted wielding and for rods of different-size branches. The eigenvectors of the inertia tensor were implicated as the basis for this haptic perceptual capability. Results were discussed in reference to information-perception specificity and its implications for effortful or dynamic touch.     

Exteroception and exproprioception by dynamic touch are different functions of the inertia tensor

When an object is held and wielded, a time-invariant quantity of the wielding dynamics is the inertia tensorIij. The 3 × 3 quantityIij is composed of moments of inertia (on the diagonal) and products of inertia (off the diagonal). Examination ofIij as a function of different locations at which a cylindrical object is grasped revealed that the products related systematically to grip position (a direction), and both the products and moments taken together related systematically to the extent of the rod to one side of the hand (a magnitude in a direction). In two experiments, observers wielded an occluded rod that was held at an intermediate point along its length and reproduced both the felt grip position and partial rod length. In both experiments, perceived grip position was a function of the rod’s products of inertia and perceived partial rod length was a function of the moments and products. Discussion focuses on the specificity of exteroception and exproprioception toIij.     

Haptic probing: perceiving the length of a probe and the distance of a surface probed.

Knowing about the properties of objects by wielding them and knowing about the distances of surfaces by striking them with objects as probes are examples of dynamic or effortful touch. Six experiments focused on the invariant mechanical parameters that couple the time-varying states (displacements, velocities) of hand-held rods to the time-varying torques and forces imposed upon them by wielding and probing. There were three major conclusions. First, when a probe is wielded without contact, perceived probe length is a function of the probe's rotational inertia; however, with contact, perceived probe length is affected by the rotational inertia and the distance of the point of contact from the probe's center of percussion. Second, when a surface is struck with a probe, perceived surface distance is affected by the probe's rotational inertia and the angle of inclination of the probe at contact. Third, under seemingly identical conditions of probing, either probe length or surface distance can be perceived selectively without confusion. Results were discussed in terms of haptic information, haptic attention, and the dynamics of probing.     

Haptic probing: Perceiving the length of a probe and the distance of a surface probed

Knowing about the properties of objects by wielding them and knowing about the distances of surfaces by striking them with objects as probes are examples of dynamic or effortful touch. Six experiments focused on the invariant mechanical parameters that couple the time-varying states (displacements, velocities) of hand-held rods to the time-varying torques and forces imposed upon them by wielding and probing. There were three major conclusions. First, when a probe is wielded without contact, perceived probe length is a function of the probe’s rotational inertia; however, with contact, perceived probe length is affected by the rotational inertia and the distance of the point of contact from the probe’s center of percussion. Second, when a surface is struck with a probe, perceived surface distance is affected by the probe’s rotational inertia and the angle of inclination of the probe at contact. Third, under seemingly identical conditions of probing, either probe length or surface distance can be perceived selectively without confusion. Results were discussed in terms of haptic information, haptic attention, and the dynamics of probing.     

Rotational inertia and multimodal heaviness perception

Perceived heaviness of wielded objects has been shown to be a function of the objects’ rotational inertia—the objects’ resistance to rotational acceleration. Studies have also demonstrated that if virtual objects rotate faster than the actual wielded object (i.e., a rotational gain is applied to virtual object motion), the wielded object is perceived as systematically lighter. The present research determined whether combining those inertial and visual manipulations would influence heaviness perception in a manner consistent with an inertial model of multimodal heaviness perception. Rotational inertia and optical rotational gain of wielded objects were manipulated to specify inertia multimodally. Both visual and haptic manipulations significantly influenced perceived heaviness. The results suggest that rotational inertia is detected multimodally and that multimodal heaviness perception conforms to an inertial model.