Rigid/non-rigid grounding and transitivity

While extant replies to Jonathan Schaffer’s putative counterexamples to the transitivity of grounding have made significant strides against the charge of transitivity failure, the replies pay insufficient attention to the common structure of the counterexamples, overlooking a deeper structural feature that contributes to their prima facie plausibility. Putative counterexamples to the transitivity of grounding, I argue, trade on the distinction between what I call ‘rigid’ and ‘non-rigid’ grounding, and confusion over how rigid and non-rigid grounding react when combined pumps the intuition that the counterexamples’ chained conclusions are false. The rigid/non-rigid grounding distinction also reveals plausible weakening inference rules that have been overlooked in treatments of the logic of grounding.     

Projective invariance and the kinetic depth effect.

Seven experiments test the assumption that, in the kinetic depth effect, observers have reliable and direct access to the equivalence of shapes in projective geometry. The assumption is implicit in 'inverse optics' approaches to visual form perception. Observers adjusted a comparison shape to match a standard shape; both standard and comparison were portrayed as in continuous rotation in space, using a graphics computer. The shapes were either plane quadrilaterals or solid prisms. The angular difference of the planes of the shapes was varied, as was the dot density of a texture in those planes. Departure from projective equivalence was measured in six studies by measuring the planar analogue of cross ratio, and in a seventh by measuring the cross ratio for points in space. Projective equivalence was not found to be perceived uniformly, except in one experiment that did not involve rotation in depth. Otherwise changes in orientation of up to 180 degrees about a single coordinate axis had no significant effect on matches in shape, while changes in orientation about more than one coordinate axis produced significant effects. The addition of texture and a change in rotation speed did not correct departures from projective equivalence.     

Early motion processes and the kinetic depth effect

It has been known for over 30 years that motion information alone is sufficient to yield a vivid impression of three-dimensional object structure. For example, a computer simulation of a transparent sphere, the surface of which is randomly speckled with dots, gives no impression of depth when presented as a stationary pattern on a visual display. As soon as the sphere is made to rotate in a series of discrete steps or frames, its 3-D structure becomes apparent. Three experiments are described which use this stimulus, and find that depth perception in these conditions depends crucially on the spatial and temporal properties of the display:

1. Depth is seen reliably only for between-frame rotations of less than 15°, using two-frame and four-frame sequences.

2. Parametric observations using a wide range of frame durations and inter-frame intervals reveal that depth is seen only for inter-frame intervals below 80 msec and is optimal when the stimulus can be sampled at intervals of about 40-60 msec.

3. Monoptic presentation of two frames of the stimulus is sufficient to yield depth, but the impression is destroyed by dichoptic presentation.

These data are in close agreement with the observed limits of direction perception in experiments using “short-range” stimuli. It is concluded that depth perception in the motion display used in these experiments depends on the outputs of low-level or “short-range” motion detectors.     

Stereokinetic effect and its relation to the kinetic depth effect.

The stereokinetic effect (SKE) has been defined and studied by nested circular patterns rotating on a turntable. Circles must appear not to rotate as they revolve, which in turn results in their appearing to translate relative to one another. A powerful illusion of object depth results even though the individual circles do not undergo an appropriate foreshortening consistent with their apparent changes in slant. It is suggested and tested that the SKE is based on the changing positions between the nested contours despite the absence of any change within each contour, whereas the kinetic depth effect (KDE) entails both kinds of change. It follows that a turntable method of presentation is not necessary, and between-contour transformations can be simulated by computer animation. Displays consisting of simple translations were shown to evoke robust depth impressions as were patterns consisting of contours of varying shapes. Comparisons of the depth, compellingness, and rigidity of matched SKE and KDE displays are reported. The SKE is taken to be paradigmatic for how the visual system perceives depth when observing small object rotations that occur in everyday situations.     

How to study the kinetic depth effect experimentally

Sperling, Landy, Dosher, and Perkins (1989) proposed an objective 3D shape identification task with 2D artifactual cues removed and with full feedback (FB) to the subjects to measure KDE and to circumvent algorithmically equivalent KDE-alternative computations and artifactual non-KDE processing. (1) The 2D velocity flow-field was necessary and sufficient for true KDE. (2) Only the first-order (Fourier-based) perceptual motion system could solve our task because the second-order (rectifying) system could not simultaneously process more than two locations. (3) To ensure first-order motion processing, KDE tasks must require simultaneous processing at more than two locations. (4) Practice with FB is essential to measure ultimate capacity (aptitude) and, thereby, to enable comparisons with ideal observers. Experiments without FB measure ecological achievement--the ability of subjects to extrapolate their past experience to the current stimuli.     

On the limits of perceptual complementarity in the kinetic depth effect

In a series of experiments, we have investigated the abilities of human observers to perceive geometric properties of moving three-dimensional objects as a function of their perspective and rotational complexities. The results indicate a decreasing ability of observers to extract metric, angular, and rigid motion as the perspectives and rotations depart from parallel projections and one-parameter central rotations. In this way, quantitative limits are suggested for the principle of perceptual complementarity suggested by Shepard (1981).     

Perceived internal depth in rotating and translating objects

Previous research has indicated that observers use differences between velocities and ratios of velocities to judge the depth within a moving object, although depth cannot in general be determined from these quantities. In four experiments we examined the relative effects of velocity difference and velocity ratio on judged depth within a transparent object that was rotating about a vertical axis and translating horizontally, examined the effects of the velocity difference for pure rotations and pure translations, and examined the effect of the velocity difference for objects that varied in simulated internal depth. Both the velocity difference and the velocity ratio affected judged depth, with difference having the larger effect. The effect of velocity difference was greater for pure rotations than for pure translations. Simulated depth did not affect judged depth unless there was a corresponding change in the projected width of the object. Observers appear to use the velocity difference, the velocity ratio, and the projected width of the object heuristically to judge internal object depth, rather than using image information from which relative depth could potentially be recovered.     

Depth capture by kinetic depth and by stereopsis

The perceived depth of regions within a stereogram lacking explicit disparity information can be captured by the surface structure of regions where disparity is explicit: stereo capture. In two experiments, observers estimated surface curvature/depth of an untextured object (a 'ribbon') superimposed on a cylinder textured with dots, the cylinder curvature being defined by disparity (stereo depth) or by motion parallax (kinetic depth: KD). With the stereo-defined cylinder, depth capture was obtained under conditions where the disparity of the ribbon was ambiguous; with the KD, cylinder depth capture was obtained under conditions where the motion flow of the cylinder was in a direction parallel to that of the ribbon. These results demonstrate yet another similarity between KD and stereopsis.     

Kinetic depth effect and identification of shape

We introduce an objective shape-identification task for measuring the kinetic depth effect (KDE). A rigidly rotating surface consisting of hills and valleys on an otherwise flat ground was defined by 300 randomly positioned dots. On each trial, 1 of 53 shapes was presented; the observer's task was to identify the shape and its overall direction of rotation. Identification accuracy was an objective measure, with a low guessing base rate of the observer's perceptual ability to extract 3D structure from 2D motion via KDE. (1) Objective accuracy data were consistent with previously obtained subjective rating judgments of depth and coherence. (2) Along with motion cues, rotating real 3D dot-defined shapes inevitably produced a cue of changing dot density. By shortening dot lifetimes to control dot density, we showed that changing density was neither necessary nor sufficient to account for accuracy; motion alone sufficed. (3) Our shape task was solvable with motion cues from the 6 most relevant locations. We extracted the dots from these locations and used them in a simplified 2D direction-labeling motion task with 6 perceptually flat flow fields. Subjects' performance in the 2D and 3D tasks was equivalent, indicating that the information processing capacity of KDE is not unique. (4) Our proposed structure-from-motion algorithm for the shape task first finds relative minima and maxima of local velocity and then assigns 3D depths proportional to velocity.     

Judgments of discrete and continuous quantity: an illusory Stroop effect

Evidence from human cognitive neuroscience, animal neurophysiology, and behavioral research demonstrates that human adults, infants, and children share a common nonverbal quantity processing system with nonhuman animals. This system appears to represent both discrete and continuous quantity, but the proper characterization of the relationship between judgments of discrete and continuous quantity remains controversial. Some researchers have suggested that both continuous and discrete quantity may be automatically extracted from a scene and represented internally, and that competition between these representations leads to Stroop interference. Here, four experiments provide evidence for a different explanation of adults’ performance on the types of tasks that have been said to demonstrate Stroop interference between representations of discrete and continuous quantity. Our well-established tendency to underestimate individual two-dimensional areas can provide an alternative explanation (introduced here as the “illusory-Stroop” hypothesis). Though these experiments were constructed like Stroop tasks, and they produce patterns of performance that initially appear consistent with Stroop interference, Stroop interference effects are not involved. Implications for models of the construction of cumulative area representations and for theories of discrete and continuous quantity processing in large sets are discussed.     

Seeing double and depth with Wheatstone's stereograms

Charles Wheatstone, in his classic paper on the invention of the stereoscope, concluded "... objects whose pictures do not fall on corresponding points of the two retinae may still appear single" (1838 Philosophical Transactions of the Royal Society of London 128 384). Soon after, Ernst Brücke, Alexandre Prévost, David Brewster, Joseph Towne, and Joseph LeConte all published disagreements with this conclusion. LeConte's objections were most frequent and most prolonged. To understand the basis of the disagreements, we conducted three experiments using Wheatstone's original stereograms and found that most stereograms produced depth perception with diplopia, which partially explains the consistency among his critics' conclusions. Most of the criticism at variance with Wheatstone's conclusion was based on research conducted outside Germany. We argue that LeConte's lack of knowledge of the German literature on vision research prevented him from considering investigating Wheatstone's experiment with a stereogram having a smaller disparity.     

Phases in Movement After-Effects and their relationship to the kinetic figural effect

Summary A Movement After-Effect (MAE) observed on a structured test figure contains generally two successive phases. The initial one is non-contingent upon the test figure and is assumed to result from an adaptation process. The second phase is shown to be contingent upon the features of the test figure and their similarity with those of the generating figure. A conditioning process is assumed to share in its appearance. In Experiment I, it is shown that the areal spread of MAE which may appear in the contingent phase is likely to result from a generalization process in which part of the test figure corresponding to an unstimulated area becomes transiently effective in generating a MAE. In Experiment II distributed practice of the MAE is shown to lead to an increase in the duration of the effect when the generating and test figures are similar. This last result suggests that the true conditioning stimulus is the generating figure as such.     

The effect of rest following massed practice of continuous and discrete motor tasks

Theories of the rest-related phenomena of reminiscence and warm-up decrement regard them as independent, being due to different factors. In this study it was found that rest following massed practice of a continuous task increased performance (reminiscence) and rest following massed practice of a discrete task lowered performance (warm-up decrement). The near-zero correlation found between the phenomena indicates that they are indeed independent and task-specific. Implications of the findings for the prediction of the effect of rest, and the fact that much motor learning and performance is task-specific, is discussed.     

The effect of information content upon the perception and after-effects of a rotating field

From an investigation of movement after-effects induced by a rotating field, it seems that the information content of the inspection field is an important determinant of the subsequent movement after-effects (M.A.E.). This finding, considered in conjunction with phenomena evoked during perception of high information content and highly redundant fields, is discussed in connection with Anstis and Gregory's (1965) work on the role of retinal stimulation in the production of M.A.E.s.     

The effect of providing choices on skill acquisition and competing behavior of children with autism during discrete trial instruction

Discrete trial instruction was carried out for three students with autism. An alternating treatments design was implemented. In one condition, teachers chose the reinforcers to be used and the order in which programs were conducted. In a second condition, students chose the order of programs and the reinforcers to be used. Speed of skill acquisition and the presence of competing behavior such as tantrums, aggression, escape attempts or idiosyncratic noncompliance responses were measured. Speed of skill acquisition did not differ between the two conditions, but competing behavior was markedly reduced during student choice conditions. Copyright © 2002 John Wiley & Sons, Ltd.