Span of attention,backward masking,and reaction time

A test pattern consisting of 0 to 15 dots and a following random dot masking pattern were presented for 5 msec each with SOAs varying between 30 and 200 msec. The subject was asked to report the perceived number of dots in the test pattern as soon as possible and to assign a confidence rating to each report. The span of attention (upper limit for 50% correct numerosity judgments) increased from 2.4 to 9.5 as the SOA increased. Backward masking reduced the reported number of dots from the actual number in the test pattern, especially with small SOAs. Reaction time increased linearly at a low rate (approximately 40 msec/dot) up to 4 dots in the test pattern and then increased linearly at a high rate (approximately 370 msec/dot) as thereported, orperceived, number of dots increased. The two different branches of the reaction time curve were considered to represent two separate processes,subitizing andcounting, as suggested by Klahr (1973), who found similar dual increase rates as a function of the actual number of dots. These findings, as well as causal inference based on partial correlations and path analysis, indicated that the reported (perceived) number of dots and confidence rating were both determined by the number of stimulus dots and the SOA and that the reaction time was determined by the so-determined perceived number of dots and level of confidence. A multistage model is proposed.     

Subitizing and counting processes in young children

Children attending the first grade in school were instructed to tell the number of dots (1–9) presented on a screen. The response latencies were related to the number of dots by two different linear relations for each subject. The first of these had a slope of about 0.1 sec/dot, was applicable for the encoding of 1–3 dots, and was taken as an indication of a subitizing process. The second linear relation was applicable for 5–9 dots and had a slope of about 1.0 sec/dot reflecting the speed of a counting process. The average intersection between the functions was located at 3.22 dots. The results were compared with earlier investigations of adult subjects who on the average subitize 6 dots and count 1 dot in about 0.4 sec. It was subitizing process being higher for adults. If the encoding of a stimulus has not been terminated within about 1.5 sec for children and adults the stimulus has instead to be identified in either a counting or an estimating process.     

Connectedness affects dot numerosity judgment: Implications for configural processing

Participants judged the number of dots in visual displays with brief presentations (200 msec), such that the numerosity judgment was based on an instantaneous impression without counting. In some displays, pairs of adjacent dots were connected by line segments, whereas, in others, line segments were freely hanging without touching the dots. In Experiments 1, 2A, and 2B, connecting pairs of dots by line segments led to underestimation of dot numbers in those patterns. In Experiment 3, we controlled for the number of freely hanging line segments, whereas Experiment 4 showed that line segments that were merely attached to dots without actually connecting them did not produce a considerable underestimation effect. Experiment 5 showed that a connectedness effect existed when stimulus duration was reduced (50 msec) or extended (1,000 msec). We conclude that connectivity affects dot numerosity judgments, consistent with earlier findings of a configural effect in numerosity processing. Implications of the role of connectedness in object representation are discussed.     

Exploring the developmental changes in automatic two-digit number processing

Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the number that contained the larger dots. If numbers are processed automatically, reaction time for dot size judgment should be affected by numerical characteristics. The results suggest that, like adults, children process two-digit numbers automatically. Based on the current findings, we propose a developmental trend for automatic two-digit number processing that goes from decomposed sequential (activation of decade digit followed by that of unit digit) to decomposed parallel processing (simultaneous activation of decade and unit digits).     

Enumeration of dots: An eye movement analysis

The present study reports the measurement of response latencies and the recording of eye movements in a task in which adults had to enumerate dots in figures that differed in number of dots (n^d = 19–23) and grouping of dots. The functional relationship between latencies per dot and mean group size was in agreement with earlier findings (van Oeffelen & Vos, 1982). Temporal information from eye movement data indicated that the relative contribution of fixation durations to overall latency was far larger than the contribution of saccades, which superseded the contribution from eyeblinks. Spatial information in the form of eye movement trajectories indicated that, in general, there occurred one or two fixations at the starting position. From this position onward, eye movements were directed toward areas of dots rather than to each dot in particular. Scanning behavior was sometimes reiterative, in the sense that groups of dots were visited more than once. The results are discussed with respect to the nature of strategies employed during a dot-enumeration task.     

The effects of onset and offset warning and post-target stimuli on the saccade latency of children and adults

Two studies, involving children (mean age = 10 years) and adults, investigated the effects of visual stimulus onsets and offsets on the latency of saccades to peripheral targets. Saccade latency was reduced when foveal stimulus onsets or offsets preceded the target. When stimulus onset occurred 100 msec after target onset, the stimulus interfered with responding, with this interference effect significantly greater for children than for adults. When stimuli were presented in the peripheral visual field facilitation and interference effects were similar for children and adults. These results were interpreted as indicating that oculomotor processes are similar in children and adults while the stimulus intake processes that follow stimulus onset at the point of fixation have a greater interference effect on children's than on adults' eye movements.     

Children’s multiplicative transformations of discrete and continuous quantities

Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving whole number concepts prior to arithmetic training. Here we report evidence that this system supports children’s predictions about the outcomes of halving and perhaps also doubling transformations. A total of 138 kindergartners and first graders were asked to reason about the quantity resulting from the doubling or halving of an initial numerosity (of a set of dots) or an initial length (of a bar). Controls for dot size, total dot area, and dot density ensured that children were responding to the number of dots in the arrays. Prior to formal instruction in symbolic multiplication, division, or rational number, halving (and perhaps doubling) computations appear to be deployed over discrete and possibly continuous quantities. The ability to apply simple multiplicative transformations to analog magnitude representations of quantity may form a part of the toolkit that children use to construct later concepts of rational number.     

Saccade latency in children and adults: Effects of warning interval and target eccentricity

Saccadic response latency to the onset of an eccentric target was studied in children (mean age = 8.7) and adults. The independent variables investigated were fixation-light offset to target-light onset warning interval (0, 100, 300, and 600 msec) and target eccentricity (5° or 15°). Both children and adults showed shorter saccade latencies under warning-interval conditions. Children were found to have longer latencies than adults with 0 or 100 msec warning intervals but to respond with as short or shorter latencies with 300 or 600 msec warning intervals. Target eccentricity effects did not interact with age, and occurred only with a lower target intensity. Children defined as poor readers could initiate a response as quickly as good readers but were less able to maintain fixation-light fixation prior to target onset.     

Strength theories of disjunctive visual detection

Zero, 1, 2, or 3 black dots are tachistoscopically presented on a white field. There are two alternative tasks: (a) to decide on the presence of each of the left, middle, and right dots (multiple detection) or (b) to decide whether any of the dots was present (disjunctive detection), The results indicate that in disjunctive detection, Ss do not add together thestrengths of the three dot positions and compare this sum to a criterion. Rather they combine theirdecisions about each dot, responding “yes” to the array, if and only if they decide “yes” to any one dot. Strength distributions appear to be invariant with respect to irrelevant stimuli. Invariance with respect to report order holds approximately. However, dots reported on first are slightly more detectable. This suggests a successive scanning process, whose rate is independent of whether a stimulus is present or absent at the position scanned.     

The perception of briefly exposed point-sources of light

Point-sources of light (dots) were exposed for 10 to 50 msec, before five dark-adapted subjects in a dimly illuminated room. During voluntary fixation with one eye, the target was exposed some 10° on the nasal side of the optic axis. The intensity X duration of all targets was 2 X threshold and they consisted of either a single dot, or a pair of dots separated by a distance that was less than that required for two-point discrimination. In two-thirds of trials both the single-dot and the two-dot targets were perceived as short thin lines of various orientation. Although individual percepts were unpredictable, there was a preferred or most likely orientation for responses to the single-dot target; this was near to the horizontal for all five subjects. There was no significant difference between the preferred orientations for single-dot targets tested at sites more than 1° apart in the visual field. When two single-dot targets, separated by about 1°, were exposed simultaneously, the orientations of the perceived lines sometimes differed by as much as 80°; occasionally, one target was reported as a dot while the other was seen as a thin line. If the single-dot was briefly exposed between two continuously visible and parallel straight lines, the target usually appeared as a thin line, parallel to the framing lines. Some of these results appear to be consistent with the hypothesis that the human visual cortex, like that of the cat and monkey, contains neurones that are orientation specific.     

The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison

Numerosity estimation and comparison tasks are often used to measure the acuity of the approximate number system (ANS), a mechanism which allows extracting numerosity from an array of dots independently from several visual cues (e.g. area extended by the dots). This idea is supported by studies showing that numerosity can be processed while these visual cues are controlled for. Different methods to construct dot arrays while controlling their visual cues have been proposed in the past. In this paper, these methods were contrasted in an estimation and a comparison task. The way of constructing the dot arrays had little impact on estimation. In contrast, in the comparison task, participants' performance was significantly influenced by the method that was used to construct the arrays of dots, indicating better performance when the visual cues of the dot arrays (partly) co-varied with numerosity. The present study therefore shows that estimates of ANS acuity derived from comparison tasks are inconsistent and dependent on how the stimuli are constructed. This makes it difficult to compare studies which utilised different methods to construct the dot arrays in numerosity comparison tasks. In addition, these results question the currently held view of the ANS as capable of robustly extracting numerosity independently from visual cues.     

Latency and accuracy characteristics of saccades and corrective saccades in children and adults

Accuracy and latency characteristics of the first saccade to a target together with the frequency and latency of corrective saccades were studied in children (mean age = 8.5) and adults. The independent variables manipulated were fixation-light offset to target-light onset warning interval (0 and 300 msec) and the presence and location of nontarget stimuli. Although saccade accuracy was significantly affected by nontarget lights, children could respond as accurately as adults and, in replication of previous findings, as quickly when a 300 msec warning interval was given. No speed-accuracy trade off was found for either group as a function of the warning signal condition. Children were as likely to make corrective saccades as adults, but did so with a significantly longer latency. Corrective saccade latencies were greater when a change in direction was required but this effect did not interact with age.     

An alphanumeric display program for a PDP-8

Alphanumeric and special characters composed of 5 by 7 dot matrices can be displayed on a cathode ray tube by use of a program written for the PDP-8 family of computers. The CRT surface is specified to contain up to 32 rows with up to 32 characters per row. The 35 dots defining each character require 1.5 msec to generate. Every possible arrangement of spatial and temporal organization among and between strings of characters can be created by simple parameter specification before each trial. The program is designed to operate with a minimal 4k-memory computer configuration, with no special hardware other than an oscilloscope display. The program also permits efficient on-line operation so that an entire experiment can be run quickly and efficiently without further programming. A large number of examples are detailed, and operating procedures are specified.     

Motion in depth: adequate and inadequate simulation

We measured errors in estimating the absolute time to collision with a simulated approaching textured object. The texture elements were circular bright dots. When we matched the rate of angular expansion of the simulated object, the rate of expansion of the texture dots, and the rate of increase of dot separation, so as to accurately simulate an approaching object, errors were small underestimations that were independent of dot size (mean of 3.2%). When dot angular size was held constant during the simulated approach, errors were the same as when the simulation was accurate, provided that dot size was less than 2.2-4.4 min of arc. As dot size was progressively increased, errors changed to overestimations. For the largest dot size used (10.5 min of arc at time t = 0), time to collision was overestimated by up to 21%. A sufficiently large overestimation would mean that measures taken to avoid collision would be too late. We suggest that the relevance to everyday life of data on the perception of motion in depth and self-motion collected using constant-sized dot displays might be questionable if dot size exceeds 2.2-4.4 min of arc.     

Cerebral asymmetries in random-dot stereopsis: reversal of direction with changes in dot size

Visual field differences in stereoscopic form recognition using Julesz-type random dot stereograms were investigated. Dot size was varied in order to test the possibility that variations in the carrier dimension have contributed to past estimates of visual field differences. Twelve male and twelve female subjects, all right-handed, appeared for three test sessions-one with each different dot size. In each session the stimuli were flashed twenty-four times in each visual field, for 120 ms. Results showed no overall visual field effect, but a highly significant interaction between visual field and dot size. For small dots, left visual field superiority was observed, as previously reported by Durnford and Kimura. With large dots, however, the right visual field was superior. This reversal of visual field differences as a function of dot size implies that there is no consistent cerebral hemispheric specialization for stereopsis or stereoscopic form recognition per se. Instead, it appears that there is relative hemispheric specialization for responding to the carrier of stereoscopic information.     

The perception of continuous curves in dot stimuli

Two categorisation experiments are reported in which the perceptual phenomenon that some simple arrays of discrete dots appear as a continuous curve whereas others are perceived as an angular contour or as consisting of separate groups of dots was investigated. Triplets of dots were presented in the first experiment, and complete or incomplete regular dot polygons (ie dots positioned on the vertices of imaginary regular polygons) in the second. In both experiments the perception of a curve versus an angle was determined mainly by the relative orientations of the dots, ie by the angles between successive virtual lines, whereas the lengths of the virtual lines had relatively little influence. In experiment 2 the number of displayed dots was shown to be a second independent factor for perceiving continuity. These results are in agreement with results from experiments on dipole textures discrimination, and suggest the psychological existence and importance of virtual lines in the visual processing of dot stimuli.     

“多少”概念发展的研究

采用数量判定任务,分别用2～30和5～100范围内点子图为刺激,研究个体“多”和“少”概念的发展。结果发现：在5～100点子条件下,随年龄的增长,个体“多”概念的判断值、“少”概念的判断值、“多”“少”概念的临界值均显著增大;7～9岁是个体“多少”概念发展的转折期;个体对“多少”概念的认知具有相对性;在本实验的两种条件下,随年龄增长,个体“多”概念的判断值、“少”概念的判断值、“多”“少”概念的临界值逐渐趋于刺激点子数最大值的2/3、1/3、1/2,“多”概念与“少”概念判断的不确定距离逐渐趋于刺激点子数最大变化范围的1/3或略小于1/3。     

Scanning,holistic encoding,and the word-superiority effect

The role of holistic encoding induced by scanning in the superior identifiability target letters in orthographic strings (words) enjoy over those in strings of unrelated letters was examined in two experiments. Both the set of potential targets and the critical position in the letter arrays were predesignated. One group in each experiment was induced to scan each array from left to right in a dot-counting task. A dot could precede the array to its left and/or appear with the array to its right. Only this group displayed the word superiority. For the second group in the first experiment, any dot(s) present always appeared with the array. The second group in the second experiment was shown no dots but, rather, performed the letter-identification task only. The absence of a word-superiority effect in other studies is related to holistic encoding stemruing from scanning requirements, and the implications for positional uncertainty explanations of the phenomenon are discussed.     

Within-modality and cross-modality attentional blinks in a simple discrimination task

Following up on studies of the "attentional blink," we studied interference between successive target stimuli in visual and auditory modalities. In each experiment, stimuli were two tones and four dots, simultaneously presented for 1,800 msec. Targets were brief intensity changes in either a tone or a dot. Subjects gave unspeeded responses. In four experiments, our results showed interference between targets in the same modality, but not across modalities. We conclude that, under our experimental conditions, restrictions in concurrent target identification are largely modality specific.     

Patterns of perceived similarity cannot be generalized from long to short exposure durations and vice versa

Subjects rated the perceived similarity between patterns and their 180-deg rotational variants. The stimuli, adapted from Halpern, Fishbein, and Warm (1979), were randomly generated dot patterns and line drawings and polygons generated from the dot patterns. Inspection time was varied in a between-subject design. As in the Halpern et al. (1979) study, it was found that the variables of form type (dots, lines, polygons) and axis of rotation (x, y, z) had no effect on perceived similarity in the long exposure conditions. However, when inspection time was limited to 150 msec, both variables had a substantial impact. This finding undermines the frequent practice of selecting stimuli for use in reaction time or other experiments with limited inspection time on the basis of similarity ratings gathered under typical free inspection conditions.