Development of children's ability to judge relative numerosity

Three- to seven-year-old chilren were trained through reinforcement to select either the more or less numerous of two rows of squares. One group was shown rows in which number covaried with row length, one group saw rows in which number covaried with row density, and a third group saw rows in which number did not covary with other dimensions. The children's operational stage was assessed by a number conservation test. All children successfully judged relative numerosity when number covaried with length or with density, but only concrete operational children were successful when number did not covary with other dimensions. Preoperational children are thus not able to base judgments of relative numerosity solely on number.     

Vicario's illusion of sloping steps reexamined

If a few parallel horizontal rows of dots are set diagonally, like steps, across the visual field, the inner rows appear not to be horizontal but sloping up to one side; the effect holds as long as the vertical distances between the rows do not exceed a given visual angle. This illusion, described by Vicario in 1978, was never explained. An experiment is reported in which the illusion was still visible at row separations well in excess of the spatial limits originally considered, provided the stimulus elements were enlarged. The maximum illusion was obtained for length ratios (interrow distance to size of dots) identical to those which have been shown to produce the largest effects in a number of illusions of area and length. This suggests that Vicario's illusion is similar to other illusions of extent, and that it can be explained by a neural extent-coding model.     

Numerical comparison processes

The relative lengths of two rows of objects systematically affected the time to make judgments of the relative number of objects. The time to decide which row contained more objects generally increased with the amount of incongruity between length and number (e.g., reaction time was long when the numerically larger row was the shorter of the two). In addition, the time to decide that the rows contained an equal number of objects increased with the disparity in length between the rows. These results suggest that length information was used in the numerical comparison process. A model that uses an internal transformation of row length is proposed to account for the results.     

Change blindness and priming: When it does and does not occur

In a series of three experiments, we explored the nature of implicit representations in change blindness (CB). Using 3 x 3 letter arrays, we asked subjects (Ss) to locate changes in paired arrays separated by 80 ms ISIs, in which one, two or three letters of a row in the second array changed. In one testing version, a tone followed the second array, signaling a row for partial report (PR). In the other version, no PR was required. After Ss reported whether a change had been detected and the PR had been completed (if required), they were asked to identify a degraded letter trigram that was either novel, or from a previously shown row (repetition priming). Our findings indicate that when CB occurs, both the pre-change and post-change stimulus information primes despite its unavailability to consciousness. Surprisingly, findings also indicate that when change detection occurs only the post-change information primes.     

Children's reasoning about spatial relational similarity: the effect of alignment and relational complexity

We investigated 4- and 5-year-old children's mapping strategies in a spatial task. Children were required to find a picture in an array of three identical cups after observing another picture being hidden in another array of three cups. The arrays were either aligned one behind the other in two rows or placed side by side forming one line. Moreover, children were rewarded for two different mapping strategies. Half of the children needed to choose a cup that held the same relative position as the rewarded cup in the other array; they needed to map left-left, middle-middle, and right-right cups together (aligned mapping), which required encoding and mapping of two relations (e.g., the cup left of the middle cup and left of the right cup). The other half needed to map together the cups that held the same relation to the table's spatial features-the cups at the edges, the middle cups, and the cups in the middle of the table (landmark mapping)-which required encoding and mapping of one relation (e.g., the cup at the table's edge). Results showed that children's success was constellation dependent; performance was higher when the arrays were aligned one behind the other in two rows than when they were placed side by side. Furthermore, children showed a preference for landmark mapping over aligned mapping.     

Great apes’ strategies to map spatial relations

We investigated reasoning about spatial relational similarity in three great ape species: chimpanzees, bonobos, and orangutans. Apes were presented with three spatial mapping tasks in which they were required to find a reward in an array of three cups, after observing a reward being hidden in a different array of three cups. To obtain a food reward, apes needed to choose the cup that was in the same relative position (i.e., on the left) as the baited cup in the other array. The three tasks differed in the constellation of the two arrays. In Experiment 1, the arrays were placed next to each other, forming a line. In Experiment 2, the positioning of the two arrays varied each trial, being placed either one behind the other in two rows, or next to each other, forming a line. Finally, in Experiment 3, the two arrays were always positioned one behind the other in two rows, but misaligned. Results suggested that apes compared the two arrays and recognized that they were similar in some way. However, we believe that instead of mapping the left–left, middle–middle, and right–right cups from each array, they mapped the cups that shared the most similar relations to nearby landmarks (table’s visual boundaries).     

Squinting with the mind’s eye: Effects of stimulus resolution on imaginal and perceptual comparisons

Subjects either viewed or visualized arrays that were divided into four quadrants, with each quadrant containing a set of stripes. In two experiments, one array contained only relatively narrow (high-resolution) stripes, and one contained only relatively thick (low-resolution) stripes. The subjects compared sets of stripes in different quadrants according to their length, spacing, orientation, or width. When the subjects visualized the arrays, they required much more time to compare high-resolution patterns than low-resolution patterns; when the subjects saw the arrays, they evaluated both types of arrays equally easily. In addition, the results from the third experiment provide strong evidence that people use imagery in this task; in one condition, the subjects evaluated oblique sets of stripes, and in another condition, they evaluated vertical and horizontal stripes. In both imagery and perception, the subjects made more errors when evaluating oblique stimuli; in imagery, they also required more time to evaluate oblique stimuli. The results suggest that additional effort is required in imagery to represent visual patterns with high resolution. This finding demonstrates that, although imagery and perception may activate common brain regions, it is more difficult to represent high-resolution information in imagery than in perception.     

Rhesus monkeys (<Emphasis Type="Italic">Macaca mulatta</Emphasis>) succeed on a computerized test designed to assess conservation of discrete quantity

Conservation of quantity occurs through recognition that changes in the physical arrangement of a set of items do not change the quantity of items in that set. Rhesus monkeys (Macaca mulatta) were presented with a computerized quantity judgment task. Monkeys were rewarded for selecting the greater quantity of items in one of two horizontal arrays of items on the screen. On some trials, after a correct selection, no reward was given but one of the arrays was manipulated. In some cases, this manipulation involved moving items closer together or farther apart to change the physical arrangement of the array without changing the quantity of items in the array. In other cases, additional items were added to the initially smaller array so that it became quantitatively larger. Monkeys then made another selection from the two rows of items. Monkeys were sensitive to these manipulations, changing their selections when the number of items in the rows changed but not when the arrangement only was changed. Therefore, monkeys responded on the basis of the quantity of items, and they were not distracted by non-quantitative manipulations of the sets.Electronic Supplementary Material Supplementary material is available for this article at     

Stereoscopic illusion based on the proximity principle

A class of ambiguous random-dot stereograms were created that share the following interesting property: Although the binocular disparity forms a periodic 'sawtooth' waveform as a function of row number (the disparity is constant for a given row), these stimuli yield a monotonically increasing depth percept along the rows. The random-dot pattern of each row is periodic along the horizontal direction for the purpose of producing an ambiguous depth percept. It is this ambiguity that makes it possible for the periodic stimulus to give rise to a monotonic percept. This monotonic percept is substantially enhanced when the rows are shown in temporal sequence instead of all being displayed together. Experiments are reported which indicate that this illusion is due to the proximity, or pulling, effect in stereopsis.     

Perceptual completion and object-based representations in short-term visual memory

Object-based representations in visual short-term memory (VSTM) were examined using a change detection memory task. A display comprising two rows of four differently colored elements was followed by a probe display in which only one of the rows reappeared. On same trials, the probed row was identical to the corresponding row in the memory display. On different trials, two of the elements in the probed row had their colors exchanged. In each memory display, a task-irrelevant visual element appeared between the two rows, with the potential to function as an occluder. Performance was enhanced when perceptual completion meant that four, rather than eight, objects were perceived in the memory display and when the probe display revealed that the occluded elements continued behind the occluder. It appears that several forms of representation can co-occur to support VSTM, one of which is object based.     

Object identification without foveal vision: Evidence from an artificial scotoma paradigm

The purpose of the present study was to investigate the degree to which foveal information is necessary for object identification. To explore this question, we used an artificial moving scotoma paradigm to eliminate a region of a currently viewed display in real time as a function of eye position. Subjects examined linear arrays of four line drawings of objects while their eye movements were recorded. Immediately following each array, a test probe was presented to test the degree to which the subject had identified those objects. Three conditions were compared, one in which a central foveal scotoma was created, one in which an extrafoveal scotoma was created, and a control condition in which the scotoma was absent. The main result was that identification accuracy was very good, but eye-movement behavior was disrupted when a foveal scotoma was present. These results suggest that foveal information is not necessary but is beneficial for perceptual encoding during object identification; the loss of foveal information can be overcome as long as compensatory extrafoveal processing is possible.     

Searching for a pre-specified target letter in briefly displayed words and unpronounceable non-words

Two experiments were designed in which subjects searched briefly displayed and masked arrays of letters for a single pre-specified target. The target was randomly located at one of twelve positions, its identity remained constant throughout, and it was embedded either in the context of words or in a context of unpronounceable strings of letters. In experiment 1 the letters were arranged in two six-item rows, and word and non-waord displays were mixed and presented to a single group of subjects. Accuracy of search was superior when the letters formed words, both for responses scored for correct position and for responses scored for correct row. In experiment 2 word and non-word displays were presented to different groups of subjects, and for both groups the twelve characters were either arranged as before in two rows or were positioned at loci representing the clock positions. Accuracy of search was again superior when the letters formed words and were arranged in rows, but there was no advantage for words when the letters formed a circle. These findings, firstly, indicated that the “word-superiority effect” obtained in experiment 1 was not a result of subjects adopting a word processing strategy for all stimuli, and secondly, they suggested that the word information could not be used to advantage in the absence of spatial cues delineating the words and/or when the letters were not positioned in the usual horizontal arrangement. It was concluded that the results of both studies were consistent with a perceptual account of the word superiority effect.     

Effects of gravitational and optical stimulation on the perception of target elevation

To examine the combined effects of gravitational and optical stimulation on perceived target elevation, we independently altered gravitational-inertial force and both the orientation and the structure of a background visual array. While being exposed to 1.0, 1.5, or 2.0 Gz in the human centrifuge at NASA Ames Research Center, observers attempted to set a target to the apparent horizon. The target was viewed against the far wall of a box that was pitched at various angles. The box was brightly illuminated, had only its interior edges dimly illuminated, or was kept dark. Observers lowered their target settings as Gz was increased; this effect was weakened when the box was illuminated. Also, when the box was visible, settings were displaced in the same direction as that in which the box was pitched. We attribute our results to the combined influence of otolith-oculomotor mechanisms that underlie the elevator illusion and visual-oculomotor mechanisms (optostatic responses) that underlie the perceptual effects of viewing pitched visual arrays.     

CHOICES FROM IDENTICAL OPTIONS

Abstract— Many of the decisions that people must make involve selections from arrays of identical options The studies presented explored people's preferences in two contexts choosing one Item from rows of identical items and choosing a route from a series of identical routes The first three studies examined preferences for items in particular positions Whether people were choosing a product from a grocery shelf, deciding which bathroom stall to use, or marking a box on a questionnaire, they avoided the ends and tended to make their selection from the middle For example, when there were four rows of a product in the supermarket, only 29% of the purchases were from the first and last rows, and 71% were from the middle two The last three studies examined whether a similar preference exists in picking a route when all of the available routes are the same length and require same number of turns In solving mazes, planning routes on maps, and walking around campus, people showed the pattern opposite to that found for choosing Items in rows They avoided the middle routes and tended to take either the first or the last one Overall, the last available route was the favorite The notion that these behaviors may minimize mental effort is explored     

Binocular depth perception in the pigeon.

By means of a discrete-trial simultaneous discrimination procedure, pigeons were trained to respond differentially to visual arrays that were identical except that one of them contained a circle displaced in depth when viewed stereoscopically. Performance was severely disrupted when one eye was occluded. The monocular deficit was peculiar to the depth task, inasmuch as no such decrement was seen on a pattern discrimination. The results imply that presence of the displaced circle was discriminated on the basis of a binocular cue. It was also found that pigeons could discriminate the direction of the displacement. Discrimination of depth was independent of the global form and still occurred when elements of the array were randomly displaced in depth. Performance was not disrupted when the absolute convergence angle of the depth stimulus was changed. The cue that consistently accounted for the behavior seen was the detection of the relative angles of convergence--that is, the retinal disparity of the two planes in depth. Thus, despite the lateral position of the eyes of the pigeon, a small binocular field mediates the binocular discrimination of near objects in depth.     

Honeybees (Apis mellifera) Remember Two Near-Target Landmark Constellations

A set of experiments tested whether honeybees can remember two different landmark constellations within the same room, or whether the two constellations are mixed together in a single composite memory. Bees were trained to find a reward location with two different landmark arrays. For example, when the blue landmark was north of the yellow one, the reward was to the east; when the yellow landmark was north of the blue one, the reward was to the west. On occasional unrewarded tests, either one of the training arrays was presented (control tests), or else a training array rotated by 90° (rotated tests). A rotated array consisted of part of one training array added to a part of the other training array. Should honeybees form a single composite memory by combining the two training arrays, they should search as much at the target location on rotated tests as on control tests. Results refute this and suggest that they had two separate memories.     

Capuchin monkeys (Cebus apella) succeed in a test of quantity conservation

Nonhuman animals demonstrate a number of impressive quantitative skills such as counting sets of items, comparing sets on the basis of the number of items or amount of material, and even responding to simple arithmetic manipulations. In this experiment, capuchin monkeys were presented with a computerized task designed to assess conservation of discrete quantity. Monkeys first were trained to select from two horizontal arrays of stimuli the one with the larger number of items. On some trials, after a correct selection there was no feedback but instead an additional manipulation of one of those arrays. In some cases, this manipulation involved moving items closer together or farther apart to change the physical arrangement of the array but not the quantity of items in the array. In other cases, additional items were added to the initially smaller array so that it became quantitatively larger. Monkeys then made a second selection from the two arrays of items. Previous research had shown that rhesus monkeys (Macaca mulatta) succeeded with this task. However, there was no condition in that study in which items were added to the smaller array without increasing its quantity to a point where it became the new larger array. This new condition was added in the present experiment. Capuchin monkeys were sensitive to all of these manipulations, changing their selections when the manipulations changed which array contained the larger number of items but not when the manipulations changed the physical arrangement of items or increased the quantity in one array without also reversing which of the two arrays had more items. Therefore, capuchin monkeys responded on the basis of the quantity of items, and they were not distracted by non-quantitative manipulations of the arrays. The data indicate that capuchins are sensitive to simply arithmetic manipulations that involve addition of items to arrays and also that they can conserve quantity.     

Spatial gating effects on judged motion of gratings in apertures.

Wallach has described in qualitative terms the movement of lines behind apertures. We related the data he obtained to the aperture problem, constructed a model of movement perception, and carried out tests of the model. Experiment 1 was a parametric study, and showed the conditions under which a reliable illusion (the barber pole illusion) of diagonal movement of lines along an aperture could be obtained, and when fluctuating judgements or veridical percepts were obtained. On the basis of this study a dipole model was constructed. The model was further developed and tested. In experiment 2 the effects of total area of stimulation were examined: diagonal gratings were viewed behind multiple apertures. In experiment 3 the effects of local signs were examined: diagonal gratings were viewed in an aperture which had edges cut in small steps and stairs, with the risers parallel to the grating, and the treads parallel to the direction of motion of the grating. Experiment 4 was designed to test a prediction about the motion aftereffect of dots near and far from the point of fixation, and the results confirmed the model. It was concluded that the model accounts for the barber pole illusion and, generally, for the movement of gratings in apertures.     

Geometrical haptic illusions revisited: Haptic illusions compared with visual illusions

Révész (1934) reported that haptic illusions were observed in almost all of the geometrical optical illusion figures. The present study reexamined seven geometrical illusions in both haptic and visual modes. In the Müller-Lyer, Ponzo, and vertical-horizontal figures, haptic illusions equivalent to the visual illusions were observed. In the Oppel-Kundt figure, a haptic illusion similar to the visual one was obtained. In the haptic Delboeuf stimuli, the size illusion of the outer circle occurred, whereas that of the inner circle did not. No haptic illusion was obtained in the Poggendorff figure. In the Zöllner figure, a haptic illusion directionally opposite to the visual one was obtained. These results show that haptic illusions do not occur in all of the geometrical illusion figures. They also suggest that haptic illusions are not necessarily mediated by visualization and that haptic processing of the figures often occurs in a manner different from vision.     

Visual field differences in the magnitude of the Oppel-Kundt illusion vary with processing time

Three experiments were performed to investigate hemispheric differences in susceptibility to the Oppel-Kundt illusion presented tachistoscopically to the two visual hemifields. Experiment 1 used a successive comparison mode, in which 16 undergraduate students indicated whether the second of two successive extents looked shorter or longer than the first. Experiment 2 (20 under-graduates) and Experiment 3 (1 commissurotomy patient) required judgments of two extents presented simultaneously. The first experiment found no significant visual field differences, although females were more susceptible than males. In the second experiment, the illusion magnitude was greater in the left visual field, and in the third experiment, it was greater in the right visual field. Post hoc analyses resolve the conflicting results and show that in all three experiments, the susceptibility of the right hemisphere declined more than that of the left hemisphere during illusion processing. An interpretation is offered in terms of two parallel processes, one that is fast, uses feature extraction, and is performed more effectively in the left hemisphere, and one that is slow, uses visuospatial analysis to compute distances between parts of the illusion figure, and is performed more effectively in the right hemisphere.