An Inverse Grip Starting Posture Gives Rise to Time-Dependent Adherence to Weber's Law: A Reply to Ganel et al. (2014)

Ganel, Freud, and Meiran (2014) report that visually guided grasping violates Weber's law, a conclusion countering a series of studies by our group showing that the early but not late stages of grasping adhere to the law (Heath, Holmes, Mulla, & Binsted, 2012; Heath, Mulla, Holmes, & Smuskowitz, 2011; Holmes & Heath, 2013; Holmes, Lohmus, McKinnon, Mulla, & Heath, 2013; Holmes, Mulla, Binsted, & Heath, 2011; see also Davarpanah Jazi & Heath, 2014). In accounting for this discrepancy, we present a basic outline of Weber's law in visually guided grasping and provide an alternate account of Ganel et al.'s findings that we believe satisfies a time-dependent adherence to the law. 

Weber's law is a principle of human perception asserting that the just-noticeable difference (JND) associated with discriminating between an original and a comparator stimulus is in constant proportion to the magnitude of the original stimulus. Moreover, the law contends that the sensitivity of detecting a change in any physical continuum is relative as opposed to absolute. Extensive evidence has shown that perceptual judgments for a range of stimulus properties (e.g., brightness, loudness, shape, size) and sensory domains (e.g., auditory, tactile, visual) produce JNDs that increase linearly with stimulus magnitude. Ganel, Chajut, and Algom (2008) provided the first study to examine whether visually guided grasping adheres to or violates Weber's law. In their study, JNDs for differently sized objects (20, 30, 40, 50, 60, and 70 mm) were computed as a function of the within-participant standard deviations of peak grip aperture (PGA), and results showed that values did not vary systematically with object size; that is, results violated Weber's law. Accordingly, the authors proposed that absolute visual information mediates visually guided grasping (Goodale & Milner, 2013). Further, in deriving their view of Weber's law in grasping, Ganel et al. contend that JNDs represent the specification of object size independent of the grasping limb (i.e., independent of the magnitude the effector must open—or close—to grasp the object). 

A series of subsequent studies by our group provided support for Ganel et al.'s (2008) contention that JNDs computed at the time of PGA violate Weber's law (Heath et al., 2011; Heath et al., 2012; Holmes & Heath, 2013; Holmes et al., 2011; Holmes et al., 2013). As well, our group showed that JNDs in the early (i.e., 10% through ∼50% of grasping time) and later (i.e., >50% of grasping time and including PGA) stages of grasping adhered to and violated Weber's law, respectively. The time-dependent adherence was interpreted within the planning/control model's contention that the early and late stages of grasping are respectively mediated via relative and absolute visual information (Glover, 2004). Furthermore, in contrast to Ganel et al.'s view that JNDs in grasping selectively represent the specification of object size, our group proposed that JNDs at any stage of a grasping response represent the resolution difference between target object size and grip aperture size. In other words, we propose that the nature of the visual information supporting comparisons between an original (i.e., the target object) and a comparator (i.e., grip aperture) stimulus determines whether grasping adheres to or violates Weber's law. Notably, such a view is based on evidence demonstrating that grasping responses unfold via feedback and/or feedforward object/effector comparisons (Paulignan, Jeannerod, MacKenzie, & Marteniuk, 1991; Ulloa & Bullock, 2003; see also Jeannerod, 1986). 

Ganel et al.'s (2014) most recent study hypothesized that the linear increase in JNDs with object size during early aperture shaping “is generated entirely by the velocity of the fingers rather than by objects' size per se” (p. 2) and is a proposal originally specified by our group (see figure 4 of Holmes et al., 2011). In other words, Ganel et al. proposed that the larger velocities required to grasp larger objects give rise to a systematic increase in JNDs independent of the visuomotor system's resolution for object size. To test their hypothesis, Ganel et al. had participants grasp differently sized objects (30, 40, and 50 mm) wherein the starting grasp posture was inverted from that used in a typical grasping study. As opposed to a pinched thumb and forefinger starting posture (i.e., that used in most work), an inverted starting posture was used such that the thumb and forefinger were fully extended. Thus, instead of an early aperture opening phase and associated increased velocities for larger objects, the inverted starting posture required an early aperture closing phase and increased velocities for smaller objects. It was reasoned that if the linear scaling of JNDs to increasing object size found in previous studies (e.g., Heath et al., 2011) relates to increased aperture velocities for larger objects, then a fully extended starting grasp posture should produce increased aperture velocities for smaller objects and thus an inverse scaling of JNDs to object size. As well, Ganel et al. employed a second experiment wherein participants adopted a starting grasp posture that was always 10 mm less than the size of the to-be-grasped target object. It was reasoned that equating the absolute starting grasp posture across the differently sized objects would produce equivalent aperture opening velocities and corollary JNDs that violate Weber's law throughout the grasping trajectory. As predicted, results for the first experiment showed that JNDs scaled inversely to object size early in the grasping response (20% and 30% of grasping time) and values in the second experiment were entirely refractory to object size. Based on these results, Ganel et al. proposed that previous studies reporting a time-dependent adherence to Weber's law “have confounded visual resolution with fingers' velocity which led to an erroneous conclusion that Weber's law affected grasping at early stages of the movement” (p. 1). 

We propose an alternative explanation for Ganel et al.'s (2014) findings based on our contention that JNDs in grasping represent the area of uncertainty that an individual is unable to discriminate between the size of an original (i.e., the target object) and a comparator (i.e., grip aperture) stimulus. Accordingly, our account holds that the results of Ganel et al.'s first experiment showing an inverse relationship between JNDs and object size demonstrates adherence to Weber's law because the starting grasp posture resulted in an inverse relationship between grip aperture size and veridical object size. In other words, the atypical starting grasp posture resulted in the area of uncertainty being greater for the small as compared with the large object (see figure 2a of Ganel et al., 2014) and thereby resulted in an inverse JND/object size relationship—a result that our framework interprets as reflecting adherence to Weber's law. Similarly, our account holds that the results of Ganel et al.'s second experiment relate to the fact that the resolution for detecting differences between grip aperture and object size was equivalent across the differently sized target objects. After all, the experimenter matched the absolute difference between the starting grasp posture and object size in advance of each trial. Thus, we interpret the inverse JND/object size relationship associated with an inverted premovement grasp posture as supporting a time-dependent adherence to Weber's law. 

We also wish to highlight that our group has shown that the early adherence of JNDs to object size is not attributed to aperture velocity. In particular, Heath et al. (2012) had participants grasp differently sized target objects (20, 30, 40, and 50 mm) in grasping time criterions of 400 and 800 ms. The basis for the grasping time manipulation was that if larger forces—and corollary velocities—are associated with increased variability in motor output (Meyer, Abrams, Kornblum, Wright, & Smith, 1988; Schmidt, Zelaznik, Hawkins, Frank, & Quinn, 1979), then the larger grasp opening velocities in the 400-ms grasping time criterion should give rise to a larger slope relating JNDs to object size. Counter to that prediction, the slopes relating JNDs to object size were equivalent across the different grasping time criterions, and both showed an early but not late scaling of JNDs to object size (cf. Heath et al., 2011; Holmes & Heath, 2013; Holmes et al., 2011; Holmes et al., 2013). In other words, results evince that JND scaling to object size is independent of the magnitude of aperture opening velocity. Further, although Ganel et al. (2014) report aperture velocities at decile increments of grasping time, the authors do not report (a) overall grasping time, (b) the timing and magnitude of peak grip aperture, and (c) peak aperture opening and closing velocities. Hence, it is not possible to contrast the peak aperture velocities (and accelerations) and time-matched JNDs reported by Heath et al. (2012) with the results of Ganel et al. Moreover, previous research has shown that the premovement grip aperture used in Ganel et al.'s experiment 1 does not result in continuous grip aperture closing (Saling, Mescheriakov, Molokanova, Stelmach, & Berger, 1996; Timmann, Stelmach, & Bloedel, 1996; see also Heath, Rival, & Binsted, 2004). Instead, grip aperture is associated with an initial closure followed by a subsequent aperture re(opening), and the timing of the initial and subsequent closure is dependent on object size. More specifically, Saling et al. (1996) showed that the initial grip-closing velocity for a small object (i.e., 22 mm) is greater than that for a large object (i.e., 67 mm)—a result attributed to early online grip aperture reorganization. This is a salient issue for the present commentary for at least two reasons. First, it is possible that the noncontinuous decrease in grip aperture associated with an inverted premovement grasp posture does not provide a direct basis for object size contrasts at decile increments of grasping time. Second, and most germane to the present commentary, the observation that an inverted premovement posture engenders online aperture reorganization is compatible with our assertion that the resolution difference between the original (i.e., the object) and comparator (i.e., the hand) stimulus renders an early adherence to Weber's law. 

Of course, we recognize that our account is one that differs conceptually from Ganel et al. (2014). Moreover, we acknowledge that a conclusive demonstration of whether grasping does (or does not) elicit a time-dependent adherence to Weber's law awaits research that is able to disentangle the visual properties of an object from the associated aperture velocities required to grasp it. For example, equating the speed/accuracy demands (see Fitts, 1954) of differently sized objects (i.e., via manipulating the depth of object grasp points) may provide a framework for determining whether early JND/object size scaling represents the visual properties of a to-be-grasped object or the aperture dynamics required to grasp it. That said, our present interpretation is that the inverted JND/object size relationship associated with an inverted premovement grasp posture is commensurate with the view that visually guided grasping elicits a time-dependent adherence to Weber's law. 

Acknowledgments

Supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada and Faculty Scholar and Academic Development Fund Awards from the University of Western Ontario. 

Commercial relationships: none. 

Corresponding author: Matthew Heath. 

E-mail: [e-mail]. 

Address: School of Kinesiology and Graduate Program in Neuroscience, The University of Western Ontario, London, Ontario, Canada.