Winding one's ps and qs: mental rotation and mirror-image discrimination

Subjects were timed as they made judgments about ps and qs (also interpretable as ds and bs) in different angular orientations. Whether these judgments were left-right mirror-image discriminations (b vs. d or p vs. q) or up-down mirror-image discriminations (b vs. p or d vs. q), the subjects' reaction times increased sharply with the angular departure of each letter from its designated normal upright orientation, a fact implying mental rotation. This was so whether the subjects responded with the letter labels themselves (e.g., b vs. d) or with the labels left versus right or top versus bottom. It was again the case when the letters were replaced by nonletter forms, in which event there was also a left visual-field advantage in reaction time. This study is therefore the first to demonstrate a mental-rotation strategy when the canonical forms to be discriminated are up-down mirror images as well as when they are left-right mirror images. In both cases, however, the task requires the ability to tell left from right, and we suggest that this is the critical ingredient that induces mental rotation.     

Kinesthetic aspects of mental representations in the identification of left and right hands

Kinesthetic aspects of mental representations of one’s own hands were investigated. Line drawings showed a human hand in one of five versions, in which finger position and wrist rotation varied; each version occurred as a left and as a right hand, and could appear in any one of eight directions in the picture plane. The subject was required to make quick judgments of whether a left or a right hand was represented, under three conditions of head tilt (left, upright, right). Reaction time varied systematically, reflecting the time required to move one’s own hand into congruence with the stimulus. Head tilt influenced the subjective reference frame of mental rotation when the degree of head tilt was 60 deg.     

Velocity-dependent improvements in single-dot direction discrimination

Thirty-six Brown University students participated in three experiments designed to address perceptual learning. In each experiment, visual discrimination thresholds were tracked over 4,200 trials. Results from Experiment 1 suggest that the pattern of threshold reduction on a single-dot motion-direction discrimination task was stimulus-direction specific and matched (in a velocity-dependent manner) the threshold reduction pattern previously reported for a line-orientation discrimination task. In Experiment 2, it was determined that the stationary-line-orientation—specific practice effects originally reported by Vogels and Orban (1985) could be replicated but were contingent on line length. Similarly, the results from Experiment 3 suggest that practice effects originally reported by Ball and Sekuler (1987) could be replicated but were contingent on stimulus velocity. Implications for the mechanisms underlying direction and orientation discrimination are considered.     

Item type,occlusion, and gender differences in mental rotation

Two experiments were conducted to examine the role of item type in mental rotation. In each experiment, participants completed two computerized mental rotation tasks, one with blocks as stimuli and one with human figures as stimuli. The tasks were formatted either as a multiple-choice psychometric test (Experiment 1) or as a same–different type task (Experiment 2). Aside from the expected replication of a decreased effect of occlusion on women's accuracy when processing human figures compared to block figures, it was hypothesized that response times would increase when processing the complex but familiar human figures, compared to the simple but unfamiliar block figures. In Experiment 1, the results relevant to occlusion were replicated. However, the presence of a speed–accuracy trade-off suggested that participants processed human figures faster but less accurately than block figures. In Experiment 2, both men and women performed faster and more accurately when processing occluded human figures than when processing nonoccluded human figures. The effect of item type, its potential link to embodied cognition, and the role of strategy selection on gender differences in mental rotation are discussed.     

Reference frames in mental rotation

Four experiments are reported that investigate whether images or reference frames are transformed during a mental rotation task. In all experiments a display of four identical letters (P1) was presented at either +90 degrees or -90 degrees from upright, and subjects had to decide whether the letters were normal or mirror-image reflections. A single letter (P2) was then presented 100 ms later in a variable orientation with the same task instructions. Reaction times to P2 were assessed to determine whether an image of P2 was rotated to upright or whether an internal reference frame was rotated into congruence with P2 from the orientation of P1. The results as a whole suggest that transformations of P2 can be initiated either relative to upright or relative to the orientation of P1. They further indicate that the probability of using each reference orientation can be changed by procedural variations. The findings are most parsimoniously interpreted as suggesting that mental rotation involves the transformation of reference frames rather than the transformation of template-like representations.     

Developmental changes in mental rotation

Subjects from Grades 3, 4, 6, and college judged whether pairs of stimuli were identical or mirror-image reversals. One stimulus of a pair was presented upright; the other was rotated 0 to 150° from the standard. The pairs were either alphanumeric symbols or unfamiliar, letter-like characters of the type found on the PMA Spatial Ability Test. Response latencies were measured. The primary results were that (a) the speed of mental rotation increased with development, (b) unfamiliar characters were rotated more slowly than alphanumeric characters, by approximately the same amount at each grade, and (c) unfamiliar characters were encoded and compared more slowly than alphanumeric symbols, by an amount that declined with development. The results are discussed in terms of the component processes that underlie developmental change and individual variation in mental rotation skill.     

The frame turns also: Factors in differential rotation in pictures

When pictures of simple shapes (square, diamond) were seen frontally and obliquely, (1) the shapes with a deeper extent into pictured space underwent morerotation (Goldstein, 1979), which is an apparent turning to keep an orientation toward an observer’s changing position; (2) there was little effect of whether the observer knew the picture surface’s orientation in real space, except that such knowledge could prevent multistability; and (3) depicted picture frames also rotated. In other experiments, figural and frame rotations were independent of each other, and rotation was shown for real frames. The rotation of depthless depictions suggests that at least two rotational factors exist, one that involves the object’s virtual depth and one that does not. The nature of this second factor is discussed. Frame rotation appeared to subtract from object rotation when the two were being compared; this could explain a paradox in picture perception: Depicted orientations often seem little changed over viewpoints, despite (apparent) rotations with respect to real-space coordinates.     

A colorful walk on the mental number line: Striving for the right direction

Verguts and Van Opstal [Verguts, T., & Van Opstal, F. (2008). A colorful walk, but is it on the mental number line? Reply to Cohen Kadosh, Tzelgov, and Henik, Cognition, 106, 558-563] cleverly explained the results of Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., & Henik, A. (2008). A synesthetic walk on the mental number line: The size effect, Cognition, 106, 548-557] as a result of different association strength between the size of a number and its color in synesthesia. Here we present three challenges to their alternative explanation, and support our original suggestion.     

Children's left parietal brain activation during mental rotation is reliable as well as specific

Some recent evidence suggests that mental rotation of characters in children aged 7 or 8 years might be lateralized to the left parietal hemisphere. An alternative statement exists, however, the finding might be completely unspecific for mental rotation but either be simply a function of task difficulty or a consequence of the use of characters as stimuli. To test these alternatives, ERPs of 24 second graders were measured twice: (a) during mental rotation with characters as stimuli and orientations of 30°, 90°, or 150° and (b) during memory scanning with characters as stimuli and set sizes of 1, 2, or 3 letters. In both cases, an amplitude modulation was found. The effect of mental rotation as a function of character orientation turned out to be lateralized to the left parietal hemisphere. The effect of memory scanning as a function of set size, however, turned out to be completely non-lateralized. Thus, children's left hemisphere activation during mental rotation is reliable as well as specific.     

Accountability and ideology: When left looks right and right looks left

Managers face hard choices between process and outcome systems of accountability in evaluating employees, but little is known about how managers resolve them. Building on the premise that political ideologies serve as uncertainty-reducing heuristics, two studies of working managers show that: (1) conservatives prefer outcome accountability and liberals prefer process accountability in an unspecified policy domain; (2) this split becomes more pronounced in a controversial domain (public schools) in which the foreground value is educational efficiency but reverses direction in a controversial domain (affirmative action) in which the foreground value is demographic equality; (3) managers who discover employees have subverted their preferred system favor tinkering over switching to an alternative system; (4) but bipartisan consensus arises when managers have clear evidence about employee trustworthiness and the tightness of the causal links between employee effort and success. These findings shed light on ideological and contextual factors that shape preferences for accountability systems.     

Gender, level of spatial ability, and lateralization of mental rotation

The present study indicates that some of the inconsistencies in studies of the lateralization of mental rotation may be a consequence of uncontrolled individual differences in the general level of spatial ability. In order to investigate the relation between spatial ability and the lateralization of mental rotation, 48 subjects (24 males and 24 females) were divided into three groups based on their performance on a standardized test of spatial ability. They then performed a lateralized two-dimensional mental rotation task. The results showed the typical mental rotation function in that angle of rotation and reaction time were linearly related. A significant spatial ability by visual field interaction indicated that subjects with low spatial ability had a left field advantage, whereas subjects with medium spatial ability showed no field advantage and subjects with high spatial ability showed a right field advantage. Gender also interacted with visual field, with males showing a left visual superiority and females an insignificant right visual field advantage. A significant three-way interaction of gender, spatial ability, and angle of rotation reflected the fact that low spatial males were more profoundly affected by rotation than the other groups. The results suggest that at least some of the inconsistent findings in studies of lateralization of mental rotation may be accounted for by differences in the level of spatial ability.     

Manual training of mental rotation

The aim of this study was to investigate the timing relations between phonological encoding that is, the generation of an abstract phonological representation of a to-be-produced utterance and the initiation of articulation. Previous research (Meyer &; Schriefers, 1991) using a picture-word paradigm suggested that, in the production of simple one-word naming responses, a speaker completes phonological encoding of the complete word before articulation is initiated. In the present study, this question was investigated for the production of German no-determiner noun phrases (e.g. roter Tisch, “red table”;). The results showed reliable facilitation effects for distractors that are identical to the first syllable of the first word of the noun phrase. For the second syllable of the first word, only weak facilitation effects were obtained. For the second word, no significant facilitation effects were obtained. However, additional analyses showed that two groups of speakers can be distinguished, one showing only facilitation effects for the first syllable of the first word, and the other showing an additional facilitation effect for the second syllable of the first word. Together with related results, our findings lead to two conclusions. First, the (phonological) word is not the lower limit of phonological encoding before articulation can be initiated. Second, speakers can adjust the size of the advance planning unit at the phonological level based on the specific speaking context.     

Coding left and right

The present study compared the processing of direction for up and down arrows and for left and right arrows in visual displays. Experiment 1 demonstrated that it is more difficult to deal with left and right than with up and down when the two directions must be discriminated but not when they must simply be oriented to. Experiments 2 and 3 showed that telling left from right is harder regardless of whether the responses are manual or verbal. Experiment 4 showed that left-right discriminations take longer than up-down discriminations for judgments of position as well as direction. In Experiment 5 it was found that position information can intrude on direction judgments both within a dimension (e.g., a left arrow to the left of fixation is judged faster than a left arrow to the right of fixation) and across dimensions (e.g., judging vertically positioned left and right arrows is more difficult than judging horizontally positioned left and right arrows). There was indirect evidence in these experiments that although the spatial codes for up and down are symmetrical, the codes for left and right may be less so; this in turn could account for the greater difficulty of discriminating left from right.     

Sex differences in mental rotation strategy

When humans decide whether two visual stimuli are identical or mirror images of each other and one of the stimuli is rotated with respect to the other, the time discrimination takes usually increases as a rectilinear function of the orientation disparity. On the average, males perform this mental rotation at a faster angular speed than females. This experiment required the rotation of both mirror-image-different and non-mirror-different stimuli. The polygonal stimuli were presented in either spatially unfiltered, high-pass or low-pass filtered versions. All stimulus conditions produced mental rotation-type effects but with graded curvilinear trends. Women rotated faster than men under all conditions, an infrequent outcome in mental rotation studies. Overall, women yielded more convexly curvilinear response functions than men. For both sexes the curvilinearity was more pronounced under the non-mirror-different, low-pass stimulus condition than under the mirror different, high-pass stimulus condition. The results are considered as supporting the occurrence of two different mental rotation strategies and as suggesting that the women were predisposed to use efficiently an analytic feature rotation strategy, while the men were predisposed to employ efficiently a holistic pattern rotation strategy. It is argued that the overall design of this experiment promoted the application of an analytic strategy and thus conferred an advantage to the female participants.     

Fear and anxiety modulate mental rotation

We used an emotional priming paradigm to investigate whether fear and anxiety modulate mental rotation of abstract three-dimensional objects (i.e., Shepard-Metzler figures). On each trial, participants viewed pairs of objects and decided whether the objects had the identical shape by mentally rotating the one on the right into congruence with the one on the left. The participants viewed a picture of a face—fearful or neutral—briefly before the pairs of objects appeared. Participants with high state anxiety, and not those with low state anxiety, rotated the objects more quickly after they saw fearful faces than after they saw neutral faces. This result not only documents that fear can improve mental rotation but also shows that this effect is modulated by the emotional arousal of the participants.     

Social psychological models of choice behavior and drivers' left turns

ABSTRACT. The authors reanalyzed data from a simulated left-turn experiment (P. A. Hancock, J. K. Caird, S. Shekhar, & M. Vercruyssen, 1991) to test the adequacy of the nonlinear Gray-Tallman satisfaction balance model of choice behavior (L. N. Gray & I. Tallman, 1984) in predicting left turns. Participants (Hancock et al., 1991) were 40 experienced U.S. drivers who were exposed to simulated oncoming traffic; the size of the vehicle (motorcycle, compact vehicle, full-sized vehicle, delivery truck), its speed (10-70 mph, or 16-112 kmph), and the intervehicle time gap (3-9 s) varied. Hancock et al. (1991) measured (a) the likelihood of a left turn and (b) the occurrence of a collision. The probability of a left turn was greater for larger intervehicle time gaps and for oncoming smaller vehicles traveling at higher speeds. The Gray-Tallman (1984) model explained 69% of the variation in turning versus 57% for a linear regression model. In making decisions people tend to treat the values and costs affecting choices in a multiplicative, rather than linear, fashion. The Gray-Tallman model also has the potential for incorporating, both theoretically and mathematically, an unlimited range of potential values and costs that may influence left turn decisions.