An investigation of the cues responsible for figure impossibility

Two different perceptual confrontations produced by two different cues (sides that seem to twist and apparent levels of depth), which were thought to influence the perception of the degree of possibility of impossible torus figures, were examined in two experiments. In Experiment 1 it was found that net change in depth experienced with one scan around the figure was inversely related to magnitude estimates of possibility, whereas the number of apparently twisted sides was not. These results were verified in Experiment 2, a replication of Experiment 1 using stereograms of the figures, in which an interpretation of multiple levels of depth was more difficult.     

Viewpoint-dependent recognition of scenes

Three experiments investigated scene recognition across viewpoint changes, involving same/different judgements on scenes consisting of three objects on a desktop. On same trials, the comparison scene appeared either from the same viewpoint as the standard scene or from a different viewpoint with the desktop rotated about one or more axes. Different trials were created either by interchanging the locations of two or three of the objects (location change condition), or by rotating either one or all three of the objects around their vertical axes (orientation change condition). Response times and errors increased as a function of the angular distance between the standard and comparison views, but this effect was bigger for rotations around the vertical axis than for those about the line of sight or horizontal axis. Furthermore, the time to detect location changes was less than that to detect orientation changes, and this difference increased with increasing angular disparity between the standard and comparison scenes. Rotation times estimated in a double-axis rotation were no longer than other rotations in depth, indicating that alignment was not necessarily simpler around a "natural" axis of rotation. These results are consistent with the hypothesis that scenes, like many objects, may be represented in a viewpoint dependent manner and recognized by aligning standard and comparison views, but that the alignment of scenes is not a holistic process.     

Visual mental rotation of possible and impossible objects

Participants were tested on two visual mental rotation tasks using three-dimensional "possible" and "impossible" shapes. Both types of stimuli can be easily encoded by their parts and how they are spatially organized. However, while possible shapes can also be easily encoded as a global image, it is more difficult to encode impossible shapes in such a way. Participants visually rotated both types of stimuli at comparable rates, reflecting that local representations were used in the process of visual mental rotation.     

Test-retest reliability of the seated Functional Rotation Test in people with Parkinson's disease: a preliminary study

This study established the test-retest reliability of a seated Functional Rotation Test monitoring hand-pointing, together with head and trunk-rotation performance, in people with Parkinson's disease. An ancillary purpose was to establish the concurrent validity between the Functional Rotation Test and an electrogoniometer. 10 males with Parkinson's disease (M age=70.5 yr.; Hoehn and Yahr staging severity ranging from II to IV) were recruited. Subjects were fitted with laser-pointing devices, sat in the Functional Rotation room, and were instructed to turn actively and point to their right (or left) as far as they could comfortably manage. Tagged projections were scored (in degrees). Testing was repeated after a brief interval. Electrogoniometer projected locations were compared with Functional Rotation Test scores. Intraclass correlation coefficients (.91 to .97) indicated excellent test-retest reliability. There was also excellent agreement between electrogoniometric and Functional Rotation Test values (Intraclass correlation coefficients=.99). Thus the Functional Rotation Test provides a replicable measure of axial rotation of head, trunk, and hand-pointing in seated subjects with Parkinson's disease.     

Mom, Let Me Play More Computer Games: They Improve My Mental Rotation Skills

This study investigated how 3-D and 2-D computer game practice and delivery as well as individual differences affect performance on two tests of mental rotation (Vandenberg Mental Rotation Test and Card Rotation Test). Sixty-one US undergraduates from the Midwest completed 4 h of either massed or distributed practice. While computer game practice improved mental rotation scores in general, women’s gains were significantly greater than men’s, and the most significant gains were accomplished when practice was massed. High mathematical ability, gender, and type of practice significantly predicted improvement scores. The findings suggest that even very minimal computer game practice may improve performance on mental rotation tasks.     

Effects of stimulus complexity on mental rotation rate of polygons

Both spatial and propositional theories of imagery predict that the rate at which mental images can be rotated is slower the more complex the stimulus. Four experiments (three published and one unpublished) testing that hypothesis found no effect of complexity on rotation rate. It is argued that despite continued methodological improvements, subjects in the conditions of greater complexity may have found it sufficient to rotate only partial images, thereby vitiating the prediction. The two experiments reported here are based on the idea of making the discriminative response sufficiently difficult so as to force the rotation of complete images. The first one scaled the similarity between standard polygons and certain systematically mutated versions. From the ratings so obtained, two levels of perceived similarity, high and low, were defined and served as separate conditions in a response-time, image rotation experiment. The second experiment tested the complexity hypothesis by examining the effect of similarity on rotation rates and its interaction with levels of complexity. The results support the complexity hypothesis, but only for the highly similar stimuli. Rotation times were also generally slower for high as compared with low similarity. It is argued that these results arise because subjects rotate incomplete images when the stimuli are not very similar.     

Visual field differences for clockwise and counterclockwise mental rotation

Geometric line drawings were presented to normal subjects in the left visual field (LVF) or right visual field (RVF) at various degrees of rotation from a centrally presented vertical standard. The task of the subject was to indicate with a reaction time (RT) response whether the laterally presented stimulus could be rotated into the vertical standard or if it was a rotated mirror image of the standard. In Study 1, an overall right hemisphere superiority was found for RT and accuracy on match trials. Most interestingly, interactions between Visual Field and Rotation Angle for the match accuracy data and between Visual Field and Direction of Rotation (clockwise or counterclockwise) for the match RT slopes were found. These interactions suggested that clockwise rotations were more readily performed in the LVF and counterclockwise rotations in the RVF, consistent with other literature for mental rotation. The purpose of Study 2 was to replicate this finding of visual field differences for rotation direction using a design in which direction and degree of rotation were varied orthogonally. No main effect of Visual Field was found. However, significant interactions between Visual Field and Rotation Angle were found for both RT and accuracy, confirming the presence of visual field differences for rotation direction in a new sample of subjects. These differences were discussed in terms of the possibly greater relevance of medially directed stimuli and a possible hemispheric bias for rotation direction, and in terms of interhemispheric transmission factors.     

Rotation of objects in pictures viewed at an angle: evidence for different properties of two types of pictorial space

As an observer views a picture from different viewing angles, objects in the picture appear to change orientation relative to the observer, but some objects change orientation more than others. This difference in rotation for different objects is called the differential rotation effect. The differential rotation is not, however, accompanied by corresponding changes in the perception of the spatial layout of objects in the picture. This lack of correspondence between the perception of rotation and the perception of spatial layout is a result of the fact that the information on a picture's surface defines two kinds of pictorial space with different properties. Rotation is perceived in terms of the pictorial space outside the picture, and spatial layout is perceived in terms of the pictorial space inside the picture.     

Test-retest reliability of the functional rotation test in healthy adults

Test-retest reliability and concurrent validity for a Functional Rotation Test, developed as a clinical tool for quantifying the extent of body rotation while sitting or standing, were evaluated with healthy adults in this study. Participants, ages 20 to 72 years (n = 36) donned laser-pointing devices, stood or sat in the center of a room calibrated for the test, and actively turned and pointed to the right (or left) as far as they could comfortably. The locations of the lasers were recorded and subsequently scored. Testing was repeated after a brief rest. Concurrent measurements between a clinical goniometer and the Functional Rotation Test were also compared. Intraclass correlation coefficients (ICCs) indicated good to excellent test-retest reliability indices, ranging from .89 to .96 for standing and .87 to .95 for sitting tests. Agreement between the Functional Rotation Test and the goniometer was excellent (ICC = 1.0). The relevance and possible applications of the Functional Rotation Test are discussed.     

Mental rotation: cross-task training and generalization

It is well established that performance on standard mental rotation tasks improves with training (Peters et al., 1995), but thus far there is little consensus regarding the degree of transfer to other tasks which also involve mental rotation. In Experiment 1, we assessed the effect of mental rotation training on participants' Mental Rotation Test (MRT) scores. Twenty-eight participants were randomly assigned to one of three groups: a "One-Day Training," "Spaced Training," or "No Training" group. Participants who received training achieved higher scores on the MRT, an advantage that was still evident after 1 week. Distribution of training did not affect performance. Experiment 2 assessed generalization of mental rotation training to a more complex mental rotation task, laparoscopic surgery. Laparoscopic surgical skills were assessed using Fundamentals of Laparoscopic Surgery (FLS) tasks. Thirty-four participants were randomly assigned to a "Full Mental Rotation Training, MRT and FLS," "MRT and FLS," or "FLS-only" group. MRT results from Experiment 1 were replicated and mental rotation training was found to elicit higher scores on the MRT. Further, mental rotation training was found to generalize to certain laparoscopic surgical tasks. Participants who obtained mental rotation training performed significantly better on mental-rotation dependent surgical tasks than participants who did not receive training. Therefore, surgical training programs can use simple computer or paper-based mental rotation training instead of more expensive materials to enhance certain aspects of surgical performance of trainees.     

Preference for upright structure in memory-traces

Summary Rotation in reproduced drawings was investigated as a function of learning and prolonged forgetting (2 1/4 years). One hundred normal persons served as subjects. Using a control situation, a preference for rotating diagonal stimulus lines into upright positions was found. Rotation was most frequent at the first learning trial and disappeared gradually with practice. During forgetting rotation reappeared spontaneously and increased with time distance from learning. There was no significant correlation between rotation observed during learning and forgetting.

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Zusammenfassung In einem Gedächtnisexperiment wurden gezeichnete Reproduktionen auf Rotationseffekte untersucht, und zwar als Funktion des Lernens und prolongierten Vergessens (bis zu 2 1/4 Jahren). Einhundert normale Personen dienten als Versuchspersonen. Mit Hilfe einer Kontrollgruppe wurde eine ausgeprägte Tendenz einer Rotation diagonaler exponierter Reizlinien in aufrecht reproduzierte Linien gefunden. Die Häufigkeit dieser Rotation war bei der ersten Reproduktion am stärksten und verringerte sich zunehmend mit der Übung bis zu ihrer Auslöschung. Während des Vergessens trat der Rotationseffekt spontan wieder auf. Seine Häufigkeit erhöhte sich mit dem zeitlichen Abstand vom Lernexperiment. Es bestand keine bedeutsame Korrelation zwischen der Rotation während des Lernens und des Vergessens.

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The original experiments were conducted in the Institute of Psychology, University of Göttingen, which was then directed by Prof. Johannes von Allesch.     

Cognitive subprocesses of mental rotation: why is a good rotator better than a poor one?

The Vanderberg-Kuse Mental Rotation Test is a standard test of mental rotation ability. Recent experiments have demonstrated that mental rotation is a complex cognitive process wherein different subprocesses (focused attention, visual scanning, perceptual decision, visual memory) play important roles in performance. We classified the population as good and poor rotators by performance of mental rotation (ns = 47: 22 men and 25 women, respectively; mean age: 20.7 yr.). To examine differences cognitive subprocesses of mental rotation of these two groups were compared. There were significant differences between poor and good rotators in performance on Raven's test and the Pieron Focused Attention test scores. The good rotators scored better because their perceptual decision-analytical intelligence (Raven) and focused attention scores were higher.     

My Art by the Numbers

The author explains his affinity for numbers as it relates to his work as an artist spanning his long career. This affinity helped him invent one of the first systems for making four-color digital prints. Having been only recently introduced to the book Number and Time, by Marie-Louise von Franz, the author finds that he is in full agreement with her depth psychology theories on number. Recounting a synchronicity that he experienced while writing this paper helped the author to understand Jung’s concept of the unus mundus, as explained by von Franz in Number and Time. He speculates that number archetypes must have evolved in human consciousness over very long periods of time and writes about the number zero as a “recent” example. The author also describes his experience of a spontaneous mathematical vision that led him to create an algorithm, which in turn led him to realize that crystals having fivefold symmetry could exist in nature, which was considered impossible at the time. The author discusses his new inventions of quasi-periodic and random tile patterns, which were inspired by 15th-century Islamic tile patterns, as they related to the aperiodic patterns invented by Roger Penrose in the 20th century. He speculates about the ability of artificially intelligent computer software to be able to generate random quasi-periodic patterns. Lastly, the author recounts a synchronistic experience that occurred during the month of his 72nd birthday, in which his work with numbers is seemingly reciprocated by nature.     

Twisting space: are rigid and non-rigid mental transformations separate spatial skills?

Cognitive science has primarily studied the mental simulation of spatial transformations with tests that focus on rigid transformations (e.g., mental rotation). However, the events of our world are not limited to rigid body movements. Objects can undergo complex non-rigid discontinuous and continuous changes, such as bending and breaking. We developed a new task to assess mental visualization of non-rigid transformations. The Non-rigid Bending test required participants to visualize a continuous non-rigid transformation applied to an array of objects by asking simple spatial questions about the position of two forms on a bent transparent sheet of plastic. Participants were to judge the relative position of the forms when the sheet was unbent. To study the cognitive skills needed to visualize rigid and non-rigid events, we employed four tests of mental transformations—the Non-rigid Bending test (a test of continuous non-rigid mental transformation), the Paper Folding test and the Mental Brittle Transformation test (two tests of non-rigid mental transformation with local rigid transformations), and the Vandenberg and Kuse (Percept Motor Skills 47:599–604, 1978) Mental Rotation test (a test of rigid mental transformation). Performance on the Mental Brittle Transformation test and the Paper Folding test independently predicted performance on the Non-rigid Bending test and performance on the Mental Rotation test; however, mental rotation performance was not a unique predictor of mental bending performance. Results are consistent with separable skills for rigid and non-rigid mental simulation and illustrate the value of an ecological approach to the analysis of the structure of spatial thinking.     

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.     

Investigating how children produce rotation and pointing movements when they learn to write letters

How do children learn to write letters? During writing acquisition, some letters may be more difficult to produce than others because certain movement sequences require more precise motor control (e.g., the rotation that produces curved lines like in letter O or the pointing movement to trace the horizontal bar of a T). Children of ages 6–10 (N = 108) wrote sequences of upper-case letters on a digitizer. They varied in the number of pointing and rotation movements. The data revealed that these movements required compensatory strategies in specific kinematic variables. For pointing movements there was a duration decrease that was compensated by an increase in in-air movement time. Rotation movements were produced with low maximal velocity but high minimal velocity. At all ages there was a global tendency to keep stability in the tempo of writing: pointing movements exhibited a duration trade-off whereas rotation movements required a trade-off on maximal and minimal velocity. The acquisition of letter writing took place between ages 6 and 7. At age 8 the children shifted focus to improving movement control. Writing automation was achieved around age 10 when the children controlled movement duration and fluency. This led to a significant increase in writing speed.     

Complexity and goodness of dot patterns varying in symmetry

Summary Two experiments were performed to specify stimulus determinants of pattern complexity and pattern goodness. Dot patterns distributed in 3×3 and 4×4 matrices with a rectilinear frame were used in Experiment 1, and dot patterns in hexagonal frameworks with a circular frame were used in Experiment 2. The patterns were invariant for transformations of rotation or reflection, and formed symmetry groups of different orders, i.e., cyclic and dihedral groups. The complexity and goodness of the patterns depended upon such stimulus variables as follows: (1) complexity decreased with the order of symmetry groups with equal weights for cyclic and dihedral groups, whereas goodness increased with the order of both symmetry groups with different weights; (2) the simplicity and goodness of patterns with a vertical axis were greater than those with a horizontal axis and those with an oblique one; (3) the complexity of the patterns that had collinear elements with equal length was rated the simplest; (4) pattern goodness increased as a function of the number of dots and the concentrations of dot to rotation/reflection axis in 3×3 and 4 × 4 matrices. Thus, complexity and goodness of pattern differed with respect to these stimulus variables.     

Influence of stimulus symmetry on visual scanning patterns

Eye movements of four Ss performing a complexity rating task in which the stimuli consisted of random shapes differing in symmetry, number of turns (sides) in the perimeter, and structural angularity were examined. It was found that for both symmetrical and asymmetrical shapes, the number of fixations and fixation time increased directly with structural complexity (number of sides). Distributions of fixations for symmetrical shapes clustered in one-half of the shapes, while the distributions of fixations for asymmetrical shapes did not exhibit this one-sided bias. No differences were found in the distributions of fixation time to either half of asymmetrical or symmetrical shapes. The findings suggest that S utilizes an organizing code in addition to the featural code in characterizing a given shape. The organizing code permits S to generate the feature code for a gwen shape on the basis of partial information.     

Influence of body roll on visually induced sensations of self-tilt and rotation

Illusory self-tilt and illusory self-motion (vection) produced by rotation of a 360 degrees visual scene about the subject's roll axis was measured as a function of the presence or absence of actual rotation of the subject during acceleration of the visual scene. Rotation of the subject to a tilt of 15 degrees was at two levels of acceleration (onset) and with or without a delay between initial rotation and subsequent return (washout) to the vertical position. In one set of conditions, visual motion and subject motion were in opposite directions (concordant) and in another set they were in the same direction (discordant). In two control conditions, the subject was rotated while the visual scene remained stationary. For concordant motion the main effect of body rotation was to reduce the time taken by the subject to indicate self-tilt as compared with the response time to visual motion alone. The magnitude of estimated self-tilt was increased by actual body tilt as could be expected from addition of the perceived actual body tilt and the illusory body tilt induced by visual rotation. This effect of augmented body tilt did not persist after the body was returned to the vertical. The magnitude of vection was not markedly influenced by body rotation and washout. For discordant motion of body and the visual scene, subjects were confused and their responses were very variable, suggesting a nonlinear visual--vestibular interaction.     

Display polarity, stimulus exposure duration, and visual lobe shape

This study investigated the effects of visual display polarity and stimulus exposure duration on visual lobe shape. Analysis showed that regardless of display polarity and exposure duration combinations tested here, visual lobe contours were slightly irregular and asymmetric, of medium roundness, with a moderately rough boundary, and horizontally elongated with a mean length-width ratio of 1.53. Visual lobes mapped with negative display polarity were significantly rounder, slightly more regular and more symmetric along the vertical axis, compared with those mapped with positive polarity. Under the different polarity conditions, there were no significant differences in visual lobe area, perimeter, boundary smoothness, and elongation. When stimulus exposure duration increased from 200 to 400 msec. and from 200 to 300 msec., there were significant increases in the visual lobe area, perimeter, roundness, boundary smoothness, and regularity. No such changes were found when duration increased from 300 to 400 msec. Exposure durations did not have a significant effect on the shape categories of elongation and horizontal symmetry for the different stimuli. There were no statistically significant interactions between polarity and stimulus exposure duration for any of the lobe shape indexes used here.