A note on rotation of axes

Differences in magnitude among the communalities of a set of tests may influence the convergence of successive approximations to the limiting hyperplanes of the configuration. A slight alteration in technique is presented, which may be useful in avoiding this effect and perhaps hastening convergence.     

A simple graphical method for orthogonal rotation of axes

A simple method of making orthogonal rotations by projecting coordinates from one plot to another is presented. An easily constructed apparatus for rapid and accurate work is described in detail. By the technique proposed 12 to 15 rotations of pairs of axes involving 20 test variables can be completed per hour by a practiced technician.     

Apparent brightness of a rotating arc-line as a function of speed of rotation

52 Ss were required to adjust the brightness of a center fixation line to equal that of the apparent brightness of an arc line viewed at a distance from the fixation point subtending an angle of 12° to the eye. Adjustments were made when the arc-line was stationary and rotating at speeds of 30, 45, 60 and 75 rpm. It was found that brightness enhancement occurred with increase in speed. This result was interpreted as supporting Ansbacher's account of distortion in the perception of moving arc-lines.     

A technique for facilitating the rotation of factor axes,based on an equivalence between persons and tests

A technique is outlined which may facilitate the rotation of factor axes to a meaningful position. It is based on certain relationships between the results of test and person factor analysis, and consists essentially of supplementing the test factor space with tests which are thetest-equivalents of persons or groups of persons. These persons may be, for instance, well-known types in the domain being investigated, or even freaks. The ways in which these persons may be selected and used to determine the final rotated position of the factor axes is discussed.     

Mental rotation as a mediator for sex-related differences in visualization

This study was designed to analyze whether Mental Rotation (MR) played a role as a mediating variable for sex-related differences in Visualization (VZ). Two psychometric tests measuring MR and VZ were applied to a representative sample of 309 males and 390 females in their last year of high school. Three non-zero correlations between sex and MR, sex and VZ, and MR and VZ were found, and the effect of sex on VZ was eliminated when MR was introduced as a covariable. When three subgroups of different VZ ability were made by dividing up the VZ distribution by the first and third quartiles, sex-differences were only found for the high-scorers group, for which previous results were replicated. Results clearly indicate that MR is a plausible mediator variable for sex differences in VZ when such differences do exist. Theoretical, methodological and practical consequences of these results are discussed.     

Memory for spatial location: Cue effects as a function of field rotation

We developed theoretical extensions of Huttenlocher, Hedges, and Duncan's (1991) category-adjustment model of human spatial memory to incorporate the use of fuzzy boundariesand cue-determined prototypes. In two experiments, people reproduced locations of dots in a circle, while the number of external reference cues varied. In Experiment 1, the task field was stable and results were consistent with the use of fixed categories unaffected by number of cues. In Experiment 2, the task field was made dynamic by rotation on most trials, with results evaluated for nonrotation trials. The large cue effects observed for angular bias were consistent with the proposed cue-based fuzzy-boundary model. Large cue effects were also observed for absolute error, consistent with a model in which proximity to cues predicts stability of memory. Results point to the key role of orientation to the task environment in determining whether categorical encoding is based on cues.     

Visual working memory as the substrate for mental rotation

In mental rotation, a mental representation of an object must be rotated while the actual object remains visible. Where is this representation stored while it is being rotated? To answer this question, observers were asked to perform a mental rotation task during the delay interval of a visual working memory task. When the working memory task required the storage of object features, substantial bidirectional interference was observed between the memory and rotation tasks, and the interference increased with the degree of rotation. However, rotation-dependent interference was not observed when a spatial working memory task was used instead of an object working memory task. Thus, the object working memory subsystem—not the spatial working memory subsystem—provides the buffer in which object representations are stored while they undergo mental rotation. More broadly, the nature of the information being stored—not the nature of the operations performed on this information—may determine which subsystem stores the information.     

Family handedness as a predictor of mental rotation ability among minority girls in a math-science training program.

Right-handed girls from nonright-handed families outperformed the other groups of minority adolescent girls enrolled in a science and technology program on a test of mental rotation ability. This target group excelled over right-handed girls with all right-handed relatives and nonright-handers. The pattern of group differences in mental rotation ability found here is consistent with those found for women with math-science training at the college level. The minority boys in the program outperformed the girls as a whole, but did not differ significantly from the right-handed girls with nonright-handed relatives. The present findings provide further support for the generality of Annett's genetic theory of handedness and brain organization, and for the interaction of genetic and environmental factors in accounting for individual differences in mental rotation ability.     

Learned taste aversions in rats as a function of delay,speed, and duration of rotation

Rats fed a saccharin solution and then rotated on a turntable showed an aversion to the saccharin solution on later testing. In the first experiment, the rats learned to avoid saccharin with delays of as much as 9 hr between drinking the saccharin and the start of rotation. The second experiment showed that the critical determinant of aversiveness of rotation was number of rotations. The rats avoided saccharin as much after rotation at high speeds for short durations as after rotation at low speeds for long durations.     

Analytic rotation to a functional relationship

It is suggested that a number of theoretical models for non-test data can be tested by factor analysis. A traditional method for transforming principal-axis factor solutions is used as an aid in making such tests; a modification of this method is suggested. Means of using all of the information in a model for the purpose of determining the transformation of the arbitrary factor solution are presented, and an illustrative example is given.The author is indebted to Dr. Ledyard R Tucker for many valuable comments and suggestions.     

Spontaneous rotation of nanoparticles in a medium

In many experiments, the effects of spontaneous rotation of nanoparticles in a medium have been observed. In the article it has been shown that the reason for the spontaneous rotation of nanoparticles in a medium may be due to an increase in rotational entropy that accompanies the increasing rotational frequencies of the nanoparticles. An equation describing the rotational motion of the nanoparticles in a medium is obtained and its solution is found. It is shown that the formation of a large number of randomly oriented nanocrystals may be a reason for the forming of an amorphous phase upon cooling a melt.     

Mental rotation: An event-related potential study with a validated mental rotation task

Event-related potentials (ERPs) were recorded while subjects performed a validated mental rotation task, taken from the cognitive psychology literature. These ERPs show a late posterior negativity relative to a baseline condition requiring all of the same perceptual and cognitive processes except for the mental rotation itself. Our tentative identification of this posterior negativity with mental rotation is further supported by the finding that it varies systematically with the amount of mental rotation required on a trial by trial basis in the experimental task. We conclude that this late negativity is an ERP marker of the mental rotation process, and that this process engages primarily posterior brain regions.     

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.     

Independent component analysis as a rotation method: A very different solution to Thurstone's box problem

In this paper we consider the well‐known Thurstone box problem in exploratory factor analysis. Initial loadings and components are extracted using principal component analysis. Rotating the components towards independence rather than rotating the loadings towards simplicity allows one to accurately recover the dimensions of each box and also produce simple loadings. It is shown how this may be done using an appropriate rotation criterion and a general rotation algorithm. Methods from independent component analysis are used, and this paper may be viewed as an introduction to independent component analysis from the perspective of factor analysis.     

Decisions about the axes of disoriented shapes

Subjects were timed as they made decisions about the location of an asterisk placed to the left, right, top, or bottom of disoriented shapes, and their reaction times were plotted as a function of the angular departure of the shapes from the upright. In Experiment 1, the shapes were letters, and the functions suggested that the subjects generally mentally rotated some internal representation of each letter to the upright in order to decide whether the asterisk was to the left or the right, regardless of whether the letters were vertically symmetrical (A, T, U, V), horizontally symmetrical (B, C, D, E), or asymmetrical (F, G, R, L). For decisions about top and bottom, mental rotation rarely occurred, although there was some evidence for it in the case of horizontally symmetrical letters. Experiment 2 showed that mental rotation was not involved when subjects made one response if the asterisk was to the left or right, and another if it was at the top or bottom. In Experiment 3, the shapes were relatively unfamiliar architectural symbols, and in this case mental rotation was most strongly induced by those decisions requiring mirror-image discrimination, that is, left-right decisions for vertically symmetrical shapes and top-bottom decisions for horizontally symmetrical ones. Taken overall, the results suggest that there are two task ingredients that may induce mental rotation: One is the labeling of the left and right sides of a disoriented shape, and the other is the discrimination of mirror images.     

The evolution of mandler's conceptual primitives (image-schemas) as neural mechanisms for space-time simulation structures

The purpose of this article is to describe parallels between Mandler's theory of conceptual development in infancy, and my theory of the maximum-power principle evolution of the neuro-algorithmic organization of the brain and cultural-level mental models. A maximum power principle prey-predator scenario depicts the dynamic selective origins of neuro-algorithms underlying Mandler's various image-schemas (conceptual primitives). It is proposed that (a) image-schemas are inherited space-time simulation structures that originate in cerebellar state estimating functions which spread to the mapping systems of the cerebrum; (b) image-schemas do not come about as the result of perceptual analytic abstractive processes as Mandler has proposed, but undergo refinement in ontogeny through experience-expectant development involving perceptual analysis; (c) Mandler's image-schemas are “state-primitives” fed forward from the cerebellum to provide tracking routines for perceptual analysis, and rapid simulations constituting representation, prediction, and control; and (d) vicarious trial and error (VTE) can be interpreted as pragmatic vector simulation using image-schematic simulation structures. A scenario connecting image-schemas with Pleistocene era auditory-vocal system evolution which supports Mandler's developmental connection between image-schemas and language is proposed. It is concluded that Mandler's theory of conceptual development is essentially correct. However, it is suggested that the further articulation of Mandler's theory would benefit from parallel statement of the evolution of underlying brain mechanisms.