Dynamic (effortful) touch

Dynamic or effortful touch is a subsystem of the haptic perceptual system (Gibson, 1966). It is the most common form of touch, hardly noticed as such, and rarely studied (until recently). Its commonplace nature is conveyed by the multiplicity of words in the lexicon needed to capture its variant forms. For example, perceiving \\(x\\) by: supporting, shaking, lifting, hefting, wielding, pushing, pulling, probing, chewing, prodding, groping, bending, stretching, striking, tugging, folding, twisting, squeezing, turning, rolling, vibrating, and so on.

Dynamic (effortful) touch addresses the nature of touch as expressed in Figures 1 and 2. Figure 1a identifies the four kinds of perceiving encompassing properties of self, environment, and self-environment relations (Turvey & Fonseca, 2014). Figure 2 identifies the moments of the mass distributions integral to the “effort of touching” in the manners of Figure 1 b and c and the attendant deformation of the body’s muscular and connective tissues. A working presumption of the theory and research summarized is that the information in support of the perceptual capabilities of Figure 1 is defined over the patterns of tissue deformation.

Figure 1: (a) Perception is of environmental properties (exteroception), body properties (proprio-ception), the environment relative to the body (exproprioception), and the body relative to the environment (proexteroception). (b) Dynamic touch examples for a hand-held object. (c) Probing the environment with an implement reveals properties of the probe and the surface probed.

## Contents

* 1 Methods for studying dynamic touch
* 2 Indifference to force magnitude, significance of force variation
* 3 Intention, attention
* 4 Definite scaling and the issue of colinearity
* 5 Shape perception by wielding
* 6 An object’s mass, an object’s heaviness
* 7 Orienting objects and limbs
* 8 The challenge of selectivity
* 9 Functional properties: perceiving affordances
* 10 Independence of local anatomy
* 11 Dynamically touching things at a distance
* 12 The medium of dynamic (effortful) touch
* 13 Learning and Expertise
* 14 Controversies in perception by dynamic touch
* 15 Suggested Readings
* 16 References

## [edit] Methods for studying dynamic touch

Research directed at dynamic (effortful) touch most commonly addresses how a person knows, without benefit of vision, properties of an object held in the hand. In the paradigm reviewed here, the object is grasped at one place and either wielded freely or held still. It is not spanned between the hands or traced along its length. (In the terminology of exploratory procedures (Klatzky & Reed, this volume), the focus here, for example, is on objects held without the hand itself being supported, so-called unsupported holding and not contour following or enclosure.)

Figure 2: (a) Calculating the mass-moments about an origin O (taken to be in the wrist for hand-held objects). (b) When an inertia tensor, defined in an xyz-coordinate system is referred to (c) the symmetry axes or eigenvectors \\(e_k\\), (d) only the principal moments of inertia or eigenvalues remain.

A number of response methods are employed to ascertain whether a property has been perceived successfully. The most common is magnitude production, which requires positioning a marker to coincide with the perceived property (e.g., length, height, width, orientation). The advantage of this method is that the quantitative response can be compared against the actual object dimension. In magnitude estimation, a standard object is assigned a value of 100 and target objects are assigned numbers scaled to it (e.g., an object that feels twice as large as the standard would receive a 200; an object that felt just a little smaller could receive a 90). Magnitude estimation can be used for any geometric property, but it is especially useful for something like weight that doesn't have a straightforward magnitude production implementation. A rating scale is typically used for more functional properties. An object is rated on a scale from 1 to 7 for how well it would serve a particular purpose. A formal test of perceptual independence evaluates the extent to which perception of one property does or does not depend on perception of another property.

In a representative experiment, a rod-like object is grasped and held at just one place along its length, as in Figure 1b. The mechanoreceptors embedded in the body’s tissues cannot, therefore, be affected by the object’s length as such but they can be affected by the object’s mass moments identified in Figure 2. Rod-like objects, of course, are but one kind of object that can be readily grasped and wielded. Other kinds are shown in Figure 3. Differences among these objects (e.g., their spatial magnitudes, material composition, geometry) have consequences for the mass moments and, perforce, consequences for perception by dynamic effortful touch.

Figure 3: (a-j) Dynamic touch experiments use object sets that vary the moments of the mass distribution. (k) Data from experiments using objects from b, c, d, and f.

## [edit] Indifference to force magnitude, significance of force variation

A telling feature of dynamic touch is its dependence upon the variation of muscular forces and its independence from the magnitude of muscular forces. As Gibson (1966, p. 127) observed:

"The mass of an object can be judged, in fact, by wielding it in any of a variety of ways, such as tossing and catching, or shaking it from side to side. One can only conclude that the judgment is based on information, not on the sensations. The stimulus information from wielding can only be an invariant of the changing flux of stimulation in the muscles and tendons, an exterospecific invariant in this play of forces. Whatever specifies the mass of the object presumably can be isolated from the change, and the wielding of the object has a function of separating off the permanent component from the changes."

In substantiation of this observation are experiments that examined perceiving the lengths of handheld rods wielded freely about (a) the wrist, (b) the elbow (with wrist firm), (c) the shoulder (with wrist and elbow firm) and (d) all three joints simultaneously (Figure 6 in Turvey, 1996). Perceived length was the same for all four conditions, suggestive of invariance detection rather than inference (from torques and movements). Allied observations are that perceiving rod length is invariant over imposed levels of acceleration and over imposed levels of drag (wielding rods in water versus in air, Pagano & Cabe, 2003).

The partnership of change and nonchange, variance and invariance, suggests, however, that a perceiver is mandated to modulate force during a bout of dynamic touching. Such modulation and its benefits have been observed and may be allied with the observation that the microstructure of wielding differs for different object properties.

An apparent challenge to the preceding is the fact that rod lengths can be perceived without intended movement (without the explicit and intended torque variations of wielding, hefting, etc.), that is, by simply holding the rod still. As an example, for rods of lengths 45, 61, 76, 91, 107, and 122 cm placed directly into the hand in the posture in which the judgments were to be made, mean perceptions were 41, 58, 77, 91, 109, and 111 cm. That absence of intended movement does not mean no-movement is key to addressing this capability. In respect to Figure 4a, the selective perception of the whole rod versus a part can be achieved in “quiet standing,” that is, without intended movement. Multifractal analysis reveals different spatiotemporal structure in the fluctuations of the body’s center of pressure at the mm/ms scale for whole and part perceiving (Palatinus et al., 2014). Force modulation could be very, very subtle.

Figure 4: Length can be perceived by (a) wielding by the torso, (b) holding with one hand, propped by two hands, the hand and knee, or the hand and an environmental support; (c) wielding one rod with another; or (d) wielding with rotations about the ankle.

## [edit] Intention, attention

For a rod held at an intermediate position 1/4, 1/2, and 3/4 along its length, one can wield to determine rod length if held at an end and wield to determine length of the rod part forward of grasp. For the set of rods used in the experiments, the mean actual length was 76 cm and the mean partial length was 37 cm. The respective mean perceptions were 76 cm and 38 cm. This apparent ability to “fractionate” objects on instruction emphasizes investigations in terms of “to intend perception of \\(x\\) requires attending to information about \\(x\\).” That rod fractions can be perceived when rods are simply held (no wielding) at different locations along their lengths underscores the theoretical challenge. The challenge is amplified if emphasis is given to 0th and 1st moments. The 0th is the same value for all hand positions. The 1st is zero at the 1/2 position.

Experiments on perceiving the sweet spot of wielded occluded rackets and rods invite similar considerations. The “sweet spot” of an implement refers to the best location along an object’s length (its center of percussion) to strike something such as a tennis ball. Perception given the “sweet spot intent” is distinguished from perception given the “length intent” both in magnitude production and in dependence on mass moments. Perceived sweet spot follows closely the value of \\(I_1\\)/static moment, both for tennis rackets of different lengths (from junior through stretch rackets) and for wooden rods with attached masses used to manipulate the moments (reviewed in Carello & Wagman, 2009).

## [edit] Definite scaling and the issue of colinearity

For rods of a fixed material and fixed diameter, magnitude productions of perceived length are ordered appropriately and in the size ranges of the experimental objects. Perception that approximates values measured by a ruler suggests the availability of information that is more definite than the information supporting merely relative scaling (in which values are correctly ordered but arbitrary). This definite scaling occurs despite apparatus-allowable responses ranging from 0 to at least twice object size, for objects as small as a cocktail stirrer, as large as a pool cue, when the mix of sizes is distributed unevenly and adaptation levels are within either a narrow or wide range and when the data points are drawn, point for point, from different participants. Figure 3k suggests that there might be a definable physical basis for this definite scaling (reviewed in Turvey & Carello, 1995). The \\(y\\)-axis is the mean perceived length of each of 48 objects differing in material heterogeneity, geometric shape, and density (Figure 3 b-f), with most affixed to a uniform handle eliminating tactile information about the objects’ width, material, shape, and other characteristics. Of note is the fact that definite scaling is evident when one rod is used to wield another (Figure 4c) and regressions are conducted such that different participants contribute the means for randomly selected rod configurations (reviewed in Carello & Turvey, 2000).

Revealing the physical basis for definite scaling is confronted by the fact that the 0th, 1st, and 2nd moments over a set of experimental objects will necessarily exhibit some degree of covariation. To confront the consequent colinearity (a) stimulus objects must be inclusive of the hypothesized candidate moments and (b) multiple regressions must be used to reveal what matters (e.g., Kingma, Langenberg & Beek, 2004). Citing complications with the preceding strategy, Cabe (2010) has advanced a radically different experimental strategy: eliminate access to all but the parameter of interest. He demonstrated length perception in a situation (rolling cylindrical objects of different lengths and radii about their longitudinal axes) where the only variable was \\(I_3\\). Cabe’s strategy had been anticipated in respect to heaviness (Shockley, Carello & Turvey (2004, Experiment 1)). The tensor objects depicted by Figure 3i are equal in mass. By situating the equally weighted crossbars at the same coordinates of the central rod they are rendered equal in static moment. They are unequal, however, in rotational inertia (their inertia tensors are different). With the objects wielded individually at their marked ends, the left variant of tensor object 3i is perceived as heavier than the right variant of tensor object 3i.

## [edit] Shape perception by wielding

Figures 3e and 3f are solid objects wieldable by their handles. Experimenters provided participants with a visible array of objects and had them simply point to a match for the wielded object. Perception was well above chance and the confusions—cylinders with rectangular parallelepipeds, cones with pyramids—were predictable on the basis of \\(I_1/I_3\\). The eigenvalue ratio for hemispheres was quite distinct and this shape was not confused with other shapes (reviewed in Turvey & Carello, 1995).

## [edit] An object’s mass, an object’s heaviness

What makes something held or moved feel heavy? Convention would say “its mass,” “how much it weighs in kg,” but investigations of dynamic (effortful) touch suggest it could be otherwise, that the answer is closer to moveable-ness or maneuverable-ness or controllable-ness.

Charpentier’s size-weight illusion has been addressed in many ways. The illusion makes clear that one’s perception of an object’s heaviness does not refer to the object’s weight. In the ecological approach to dynamic touch the so-called illusion is a point of entry into the haptic perception of what a hand-held object affords by way of neuromuscular control. Tensor objects of the kind shown in Figure 3i were introduced to study heaviness perception’s dependence on the inertial eigenvalues (Figure 2d; reviewed in Turvey & Carello, 1995). Experiments have varied the mass \\(M\\) of the tensor objects and, independently, two scalar variables, symmetry \\(S = 2I_3/(I_1 + I_2)\\) and volume \\(V = 4π/3(Det I_{ij})^{-1/2}\\) of their inertia ellipsoids (reviewed in Turvey & Carello, 2011). The latter are physical characterizations of an object’s resistance to rotational acceleration taken in reference to the movement system. Arguably, they are the right degrees of freedom (the inertia tensor per se is not). They bear, respectively, on the patterning and level of muscular forces needed to move a handheld object in a controlled fashion. The experiment revealed additive effects of mass and \\(S\\) and \\(V\\). Using single rods that could be systematically varied in 0th, 1st, and 2nd moments, Kingma, Beek, and Dieën (2002) linked heaviness perception (on grounds of multiple regression analysis) to mass (0th) and static moment (1st) with no contribution from moments of inertia (2nd). In three experiments (one of which was noted above), Shockley et al. (2004) varied only the 2nd moment (in the \\(S\\) and \\(V\\) forms). The experiments revealed that variation of the 2nd moment is sufficient for heaviness perception and variation in the 0th and 1st moments is unnecessary. The perennial question of “What feels heavier, a pound of feathers or a pound of lead?” has been addressed in the foregoing terms (Wagman, Zimmerman, & Sorric, 2007).

The observations of a change in perceived heaviness for a fixed mass have a complement in weight metamers: objects of different mass that have the same perceived heaviness (reviewed in Turvey & Carello, 2011). As shown in Figure 5, combinations of mass, \\(S\\) and \\(V\\) yield metameric planes. Length perception by wielding a given object is different from heaviness perception (Amazeen, 1997, 1999). It can be expected therefore that metamers for heaviness are not metamers for length, an expectation that was confirmed (Shockley et al., 2004, Experiment 5).

Figure 5: The line for a single mass intersects three different planes yielding three levels of perceived heaviness. All points on a given plane feel equally heavy despite being different masses.

## [edit] Orienting objects and limbs

Perception of a nonvisible object’s orientation in the hand can be related to the orientation of the object’s eigenvectors \\(e_i\\) (Figure 2c; reviewed in Turvey & Carello, 1995). The perception of limb orientation might be similarly based. The arm’s inertial quantities can be manipulated through a hand-held rod extending along the underside of the arm with a cross bar to which masses can be added (reviewed in Turvey & Carello, 2011). Masses evenly distributed on the left and right keeps the ellipsoid aligned with the long axis of the arm. Uneven distribution of those masses diverts the ellipsoid from the arm’s axis. In such a case, an individual asked to point at a visible target with the occluded arm points with \\(e_i\\). Matching the positions of the left and right arms when splints are held in the two hands also result in matching the ellipsoids of the two limbs rather than matching the angles of the joints. The most recent experiments reveal, however, that these phenomena are based in the center of mass vector, \\(V_{cm}\\), of the arm and not in its eigenvector, \\(V_{e_i}\\). The two cross bars in Figure 3j allow manipulations of added masses that disentangle \\(V_{cm}\\) and \\(V_{e_i}\\) and show the former to be the constraining invariant in matching joint angles (van de Langenberg, Kingma & Beek, 2007), pointing (van de Langenberg, Kingma & Beek, 2008), and phase in interlimb rhythmic coordination (Silva & Turvey, 2012). These outcomes challenge a general inertia-tensor based theory of perceiving limb orientation.

## [edit] The challenge of selectivity

An object grasped other than at the end has, in effect, two extents, one on either side of the grasp. These two extents can be perceived reliably. If a mass is attached to the left of the grasp, that rod segment will feel longer than the rod segment on the right. If the configuration is flipped, the partial length perceptions of the segments will be flipped (reviewed in Carello & Turvey, 2000; Turvey & Carello, 1995). The working hypothesis from the inertia tensor perspective has been that distinct consequences for the mass distribution are found in the orientation of \\(e_i\\). There is, however, just one inertia tensor for a given object. To distinguish reliably left from right requires something that entails a sign change of \\(e_i\\). One conjecture is that the spinor theory of mechanical rotations, as a supplement to the inertia tensor, provides a solution within rotational dynamics. Whereas the tensor quantifies an object’s resistance to being rotated, the spinor quantifies an object’s orientation relative to some reference frame (e.g., the hand). The spinor entails two oppositely oriented orientations relative to the grasp. In this context, selective perception requires selection of one of the two distinctly oriented rotations (reviewed in Turvey, 1996)

Selective perception is also at work when someone perceives different properties of the same object. An individual can successfully perceive by wielding an object’s whole length, the partial length in front of the grasp, where the hand is on the object (reviewed in Turvey & Carello, 1995), the object’s orientation relative to the hand, and the object’s heaviness. All of the perceived properties have been shown to scale to moments of the mass distribution. Experiments by van de Langenberg, Kingma & Beek (2006) suggest that we should expect the involvement of any given moment in these cases of selective perception to be conditional on its salience in the act of wielding.

Mass moments are affected by whole length, grasp location, object orientation, and mass. Perhaps perceiving x derives from perceiving y and z (e.g., perceiving partial length depends on perceiving whole length and grasp position). Formal procedures for evaluating perceptual independence require (a) that the properties of interest be obtained for each experimental object, (b) that the properties be manipulated categorically (short, middle, long length; near, middle, far grasp; light, medium, heavy mass), and (c) that the focal properties vary orthogonally (Amazeen, 1999). For example, small, medium and heavy mass should each accompany short, middle, and long whole length. Building orthogonality into the experiment can reveal independence otherwise obscured by the shared underlying mass-distribution constraints.

Complementary analytic procedures evaluate the extent to which perception of property A depends on the value of property A, the value of property B, and perception of property B (e.g., the extent to which perception of partial length depends on actual partial length, where the grip really is, and perception of where the grip is). These procedures have revealed the following to be perceptually independent: whole length and partial length; partial length and grip position; whole length and grip position; heaviness and whole length (e.g., Cooper, Carello, & Turvey, 2000). These observations suggest that selective perception is reliable and constrained in a principled way by particular invariants manifest in the act of wielding.

## [edit] Functional properties: perceiving affordances

One can look at rotational inertia from the perspective of its relevance for controlling movement (reviewed in Carello & Wagman, 2009). With \\(S = 2I_3/(I_1 + I_2) ≈ 1\\), a hand held object affords, in Gibson’s (1986) sense, being moved as easily in one direction as in any other). Experiments on weight perception can be conducted with the alternate question of how movable is a given object— tapping into distinctions of how moving is to be accomplished (e.g., pushed or wielded, using one hand or two). Objects rated with respect to their affordance for striking with power or aiming with precision differ in their particular inertial configurations. They can be tailored to these tasks by allowing an individual to vary grasp position, in effect, changing a “hammer” into a “poker.” Moreover, distinct relations among the mass moments functions can produce metamers for hammer-with-ability that are different from metamers for poke-with-ability (Wagman & Shockley, 2011).

## [edit] Independence of local anatomy

The hand can be considered an expert wielder. It is how objects are usually grasped and maneuvered. The logic of tissue deformation, however, does not convey a special advantage on any part of the body. An object attached to the body will deform tissues in a way that reflects the object’s mass distribution. Rod length perception is invariant over the four conditions of Figure 4b. Perception of lengths of rods in Figure 4d, whole and partial (e.g., that leftward of foot), is comparable to such perception for handheld wielded rods (e.g., Hajnal, Fonseca, Kinsella-Shaw et al., 2007). It is similarly the case for postural wielding depicted in Figure 4a (Palatinus, Carello, & Turvey, 2011).

Mechanoreceptor changes with age have consequences for spatial acuity and vibration sensitivity. The ability to perceive properties by dynamic touch (specifically, length and sweet spot), however, does not differ dramatically between the old and young (reviewed in Carello & Wagman, 2009). Their judgments are single-valued functions of the same invariants and their definite scaling is in the same range. Moreover, old-young plots (regressions of length judgments by the old on length judgments by the young) are linear. The field of geriatric research takes linear old-young plots as an indication that the process underlying an achievement is the same. In this case, such an interpretation means that differences in sensory machinery between old and young do not enforce differences in how they perceive properties by dynamic touch.

Case studies of certain clinical conditions that bring about sensory neuropathy — a loss of feeling, typically in the extremities — also show that dynamic touch is preserved. A participant with a complete loss of sensitivity in one arm due to lesions on one side of the dorsal column system successfully perceived length by dynamic touch with that arm (Carello, Silva, Kinsella-Shaw, & Turvey, 2009). On a stereognosis test with that arm (identifying three-dimensional objects placed in the hand), the participant’s score was 0.

Figure 6: Experimental investigations of dynamic touch at a distance.

## [edit] Dynamically touching things at a distance

The centrality of dynamic touch to everyday activity is obscured by the fact that it is usually an aspect of a coordinated enterprise among perceptual systems. Exploratory or goal-directed contacts with an occluded surface by means of an occluded handheld probe provide a minimal example (reviewed in Turvey & Carello, 1995). Investigations of probing a horizontal surface at variable depth used a probe (Figure 6a) that varied in moment of inertia, center of percussion and angle of inclination to the surface. Perceived depth was one single-valued function of the variables, perceived probe length was another. Perception of a vertical surface’s distance and perception of a handheld probe’s length are summarized in Figure 6b. Extending tangible affordances, probing with a rod (without benefit of vision or sound) reveals whether an inclined surface affords upright standing (Figure 6c) and whether a gap in a surface affords crossing (Figure 6d).

A canonical case of dynamical touching at a distance is that of a spider in its web. A minimal simulation is possible. It can be shown that for an object on a single taut strand (Figure 6e) its distance from the participant’s hand is perceptible whether this minimal haptic web is put into vibration by the participant or by the object (via the experimenter). A theoretically special case is dynamical touching of an aperture at a distance by means of a probe with the intent to perceive the aperture’s size (Figure 6f). A single scalar quantity connects the muscle forces imposed upon the probe to the reactive forces impressed upon the tissues of the body. Perception proves to be a single-valued function of this quantity but it is not of “aperture size.” It seems to be of “size-at-a-distance-contacted-with-a-particular-implement”!

## [edit] The medium of dynamic (effortful) touch

Air and water, the media for the other perceptual systems, share the features of being homogeneous (physical properties are place invariant) and isotropic (physical properties are direction invariant) making them appropriate to being reliably structured by events that tie the perceiver to the environment. The body interpreted as a tensegrity architecture — continuous tension elements and intermittent compression elements at all of the body’s scales — promises the requisite homogeneity and isotropy for the medium of haptic perception. Turvey and Fonseca (2014) suggest that this tension array is information about, in the sense of specificity to, the layout of the body, its transformations, and its attachments. By hypothesis, the haptic medium grounds the phenomena of dynamic (effortful) touch.

## [edit] Learning and Expertise

Even though the dominant hand is more expert at wielding objects than the non-dominant hand, and the hand is more expert than the foot or torso, these differences do not alter the invariants these effectors extract. The role of specific expertise seems task-dependent. While experts and novices do not differ in inertial constraints on perceived length or sweet spot of tennis rackets or in rating whether weighted hockey sticks are suitable for intercepting a puck, they do differ in preferences for sticks suitable for hitting (Hove, Riley, & Shockley, 2010). However, novices’ preferences become “more expert” after minimal opportunities to use hockey sticks to hit pucks and intercept projectiles.

In addition to attunement, learning involves changes in calibration to environmental properties (reviewed in Wagman & Chemero, 2014). Although initial responses are already definitely scaled, responses are recalibrated after training: The slope of the perceived length/actual length regression approaches 1. Training may be visual or auditory. A magnitude estimation of length might be followed by the experimenter’s indicating actual length with a visible marker or with sounds from the object dropping onto a surface. Haptics has also been shown to “train itself” through changes in grasp position, a recalibration that transfers across properties (e.g., calibrating perceived length incidentally calibrates perceived partial length).

A theoretical context for learning in dynamic touch settings conjectures an information space as a navigable low-dimensional manifold (e.g., Jacobs, Silva, & Calvo, 2009; Michaels, & Isenhower, 2011a, b), built from moments of the mass distribution that might be relevant to a property. Learning entails moving through the information space toward the optimal locus for that task as the perceiver becomes attuned to the invariants specific to their intentions (e.g., from \\(I_1\\) towards \\(I_1/I_3\\) for perceived length). But in order for attunement to happen, tissue must be deformed reliably by distinct properties in the first place, allowing learning to be an information-guided process rather than a trial-and-error search (Michaels et al., 2008).

## [edit] Controversies in perception by dynamic touch

It is noncontroversial that dynamic touch allows awareness of a wide variety of extero-, proprio-, exproprio- and proextero-specific properties (Figure 1). But controversies arise with respect to:

* how those properties are perceived
* what kind of variable matters (higher-order invariant or collection of cues)
* how a variable that matters is used (detection or cue weighting and inference)
* whether scaling is just relative or definite (If scaling is definite, is it just in the approximate ballpark or is it consistent as well? Can manipulations make scaling more absolute?)

The preceding issues are addressed within two primary perspectives on dynamical (effortful) touch, the Cognitive and the Ecological. Both are challenged by the phenomena, but in different ways.

The cognitive perspective is commonplace. It is typically in the tradition of Helmholtz. It assumes abductive inference: the making of inferences from effects to cause. Assumed but unexplained is knowledge of the causes. It is quite likely that, as computational problems, those posed by dynamical (effortful) touch are insoluble. They are NP Hard problems, meaning they are noncomputable (N) in polynomial (P) time. Instead, computation time increases exponentially with the size of the input (e.g., time-varying tissue deformation values).

The ecological perspective is not commonplace. It is in the newer tradition of Gibson. It assumes lawfulness, namely, specificity of the deformation of the body's tissues to dynamically touched objects and specificity of the concordant perception to the dynamically touched objects contributing causally to that deformation. Assumed but undefined is the nature of the lawfulness. The physical and mathematical problems posed by dynamical (effortful) touch are intractable in the dictionary sense of not easily solved. They cross multiple length and time scales, are nonlinear, and entail mixtures of thermodynamic and mechanical principles.

## [edit] Suggested Readings

Summaries of much of the cited research and theorizing are to be found in the following articles.

* Carello, C and Turvey, M T (2000). Rotational dynamics and dynamic touch. In: M Heller (Ed.), Touch, Representation and Blindness (pp. 27-66). Oxford: Oxford University Press.
* Carello, C and Turvey, M T (2004). Physics and psychology of the muscle sense. Current Directions in Psychological Science 13,: 25-28.
* Carello, C and Wagman, J B (2009). Mutuality in the perception of affordances and the control of movement. In: D Sternad (Ed.), Progress in Motor Control: A Multidisciplinary Perspective (pp. 273-292). New York: Springer Verlag.
* Carello, C; Silva, P L; Kinsella-Shaw, J M and Turvey, M T (2009). Sensory and motor challenges to muscle-based perception. Brazilian Journal of Physical Therapy 12: 339-350.
* Turvey, M T and Carello, C (1995). Dynamic touch. In: W Epstein and S Rogers (Eds.), Handbook of Perception and Cognition, Vol. V. Perception of Space and Motion (pp. 401-490). San Diego: Academic Press.
* Turvey, M T (1996). Dynamic touch. American Psychologist 51: 1134-1152.
* Turvey, M T and Carello, C (2011). Obtaining information by dynamic (effortful) touching. Philosophical Transactions of the Royal Society B: Biological Sciences 366: 3123-3132.
* Turvey, M T and Fonseca, S T (2014). The medium of haptic perception: A tensegrity hypothesis. Journal of Motor Behavior 46: 143-187.

## [edit] References

* Amazeen, E (1997). The effects of volume on perceived heaviness by dynamic touch: With and without vision. Ecological Psychology 9: 245-263.
* Amazeen, E (1999). Perceptual independence of size and weight by dynamic touch. Journal of Experimental Psychology: Human Perception & Performance 25: 102-119.
* Cabe, P A (2010). Sufficiency of longitudinal moment of inertia for haptic cylinder length judgments. Journal of Experimental Psychology: Human Perception & Performance. 36: 373-394.
* Carello, C and Turvey, M T (2000). Rotational invariants and dynamic touch. In: M Heller (Ed.), Touch, Representation and Blindness (pp. 27-66). Oxford: Oxford University Press.
* Carello, C and Wagman, J B (2009). Mutuality in the perception of affordances and the control of movement. In: D Sternad (Ed.), Progress in Motor Control (pp. 273-292). New York: Springer Verlag.
* Carello, C; Silva, P L; Kinsella-Shaw, J M and Turvey, M T (2009). Sensory and motor challenges to muscle-based perception. Brazilian Journal of Physical Therapy 12: 339-350.
* Cooper, M; Carello, C and Turvey, M T (2000). Perceptual independence of whole length, partial length, and hand position in wielding a rod. Journal of Experimental Psychology: Human Perception and Performance 26: 74-85.
* Gibson, J J (1966). The Senses Considered as Perceptual Systems. Boston: Houghton Mifflin.
* Gibson, J J (1986). The Ecological Approach to Visual Perception. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. (Original work published in 1979.)
* Hajnal, A; Fonseca, S T; Harrison, S; Kinsella-Shaw, J M and Carello, C (2007). Comparison of dynamic (effortful) touch by hand and foot. Journal of Motor Behavior 39: 82-88.
* Hove, P; Riley, M A and Shockley, K (2006). Perceiving affordances of hockey sticks by dynamic touch. Ecological Psychology 18: 163-189.
* Jacobs, D M; Silva, P L and Calvo, J (2009). An empirical formalization of the theory of direct learning: The muscle-based perception of kinetic properties. Ecological Psychology 21: 245-289.
* Kingma, I; Beek, P J and van Dieën, J H (2002). The inertia tensor versus static moment and mass in perceiving length and heaviness of hand-wielded rods. Journal of Experimental Psychology: Human Perception and Performance 28: 180-191.
* Kingma, I; van de Langenberg, R and Beek, P J (2004). Which mechanical invariants are associated with the perception of length and heaviness of a nonvisible handheld rod? Testing the inertia tensor hypothesis. Journal of Experimental Psychology: Human Perception and Performance 30: 346-354.
* Michaels, C F and Isenhower, R W (2011a). An information space for partial length perception in dynamic touch. Ecological Psychology 23: 37-57.
* Michaels, C F and Isenhower, R W (2011b). Information space is action space: Perceiving the partial lengths of rods rotated on an axle. Attention, Perception, & Psychophysics 73: 160-171.
* Michaels, C F; Arzamarski, R; Isenhower, R and Jacobs, D M (2008). Direct learning in dynamic touch. Journal of Experimental Psychology: Human Perception and Performance 34: 944-957.
* Pagano, C C and Cabe, P A (2003). Constancy in dynamic touch: Length perceived by dynamic touch is invariant over changes in media. Ecological Psychology 15: 1-17.
* Palatinus, Z; Carello, C and Turvey, M T (2011). Principles of selective perception by dynamic touch extend to the body. Journal of Motor Behavior 43: 87-93.
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