Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size interfered with judgments of which array had more circles. Experiment 2 used displays in which circle size varied within and between arrays. Between-array differences in the amount of ''circle stuff'' (area occupied by circles) interfered with judgments of number. Experiment 3 examined whether variation in number also interferes with judgments of area. Interference between discrete and continuous stimulus dimensions occurred in both directions, although it was stronger from the continuous to the discrete than vice versa. These results bear on interpretations of studies with infants and preschoolers wherein subjects respond on the basis of continuous quantity rather than discrete quantity. In light of our results with adults, these findings do not license the conclusion that young children cannot represent discrete quantity. Absent data on attentional hierarchies and speed of processing, it is premature to conclude that infant and child quantity processes are fundamentally different from that of adults.attention ͉ child development ͉ estimation ͉ interference ͉ quantity T he capacity to represent both discrete and continuous quantity is found in both humans and nonhuman animals (1-3). Discrimination functions in animals and humans yield similar variability signatures for different dimensions of quantification (time, number, distance, and size), suggesting the use of a common representational format across species (4-7) and domains (discrete vs. continuous quantity).Questions of when in development different quantitative dimensions are represented and how these representations interact have become important issues in research on the development of numerical cognition in humans. On one view, preverbal numerical representations like those found in nonhuman animals are present at a very early age and form the basis for children's later numerical accomplishments, such as counting and the understanding of arithmetic operations (ordination, addition, and subtraction). Consistent with this view are reports that infants discriminate numerically small sets of one to three items (8-10), and larger pairs, like 8 vs. 16 (11). They also respond appropriately to the effects of addition and subtraction (12) and show intermodal numerical matching (13) and intermodal addition (14).The alternative view is that the ability to represent number (discrete quantity) appears late in development. On this view, infants' behavior in ostensibly numerical experiments is controlled by variation along covarying nonnumerical continuous dimensions of the stimuli (15). Discrete displays span various lengths, and the items cover varying amounts of surface or occupy varying volumes. Studies designed to investig...

Saccadic eye movements and perceptual attention work in a coordinated fashion to allow selection of the objects, features or regions with the greatest momentary need for limited visual processing resources. This study investigates perceptual characteristics of pre-saccadic shifts of attention during a sequence of saccades using the visual manipulations employed to study mechanisms of attention during maintained fixation. The first part of this paper reviews studies of the connections between saccades and attention, and their significance for both saccadic control and perception. The second part presents three experiments that examine the effects of pre-saccadic shifts of attention on vision during sequences of saccades. Perceptual enhancements at the saccadic goal location relative to non-goal locations were found across a range of stimulus contrasts, with either perceptual discrimination or detection tasks, with either single or multiple perceptual targets, and regardless of the presence of external noise. The results show that the preparation of saccades can evoke a variety of attentional effects, including attentionally-mediated changes in the strength of perceptual representations, selection of targets for encoding in visual memory, exclusion of external noise, or changes in the levels of internal visual noise. The visual changes evoked by saccadic planning make it possible for the visual system to effectively use saccadic eye movements to explore the visual environment.

Natural scenes are explored by combinations of saccadic eye movements and shifts of attention. The mechanisms that coordinate attention and saccades during ordinary viewing are not well understood because studies linking saccades and attention have focused mainly on single saccades made in isolation. This study used an orientation discrimination task to examine attention during sequences of saccades made through an array of targets and distractors. Perceptual measures showed that attention was distributed along saccadic paths when the paths were marked by color cues. When paths were followed from memory, attention rarely spread beyond the goal of the upcoming saccade. These different distributions of attention suggest the involvement of separate processes of attentional control during saccadic planning, one triggered by top-down selection of the saccadic target, and the other by activation linked to visual mechanisms not tied directly to saccadic planning. The concurrent activity of both processes extends the effective attentional field without compromising the accuracy, precision, or timing of saccades.

Saccades aimed at spatially extended targets land reliably at central locations determined by pooling information across the target shape [Melcher, D., & Kowler, E. (1999). Shape, surfaces and saccades. Vision Research, 39, 2929-2946; Vishwanath, D., & Kowler, E. (2003). Localization of shapes: Eye movements and perception compared. Vision Research, 43, 1637-1653]. Previous findings of saccadic errors when attempting to look at a target in the midst of distractors encouraged suggestions that pooling occurs indiscriminately, with little or no influence of a selective filter to eliminate the influence of nearby distractors. To determine the effectiveness of filtering, saccadic localization was studied for saccades made to a set of target elements (discs) interleaved with an equivalent set of distractors of a different color. With such interleaved elements, selection and spatial pooling are constrained to occur over the same spatial region. The results showed that filtering was effective and saccadic landing position was determined mainly by the target elements. Concurrent perceptual judgments made about the same stimuli (estimating the mean size of either target or distractor discs) showed better performance for the target discs than distractors, confirming that perceptual attention was allocated to the set of target elements. These results: (1) support the role of attention in setting the input to the spatial pooling process that guides saccades to spatially extended targets, and (2) show that perceptual judgments of mean value, often thought to impose modest attentional demands, are not immune to the constraints of this pre-saccadic filter.

Selective attention is closely linked to eye movements. Prior to a saccade, attention shifts to the saccadic goal at the expense of surrounding locations. Such a constricted attentional field, while useful to ensure accurate saccades, constrains the spatial range of high-quality perceptual analysis. The present study showed that the attention could be allocated to locations other than the saccadic goal without disrupting the ongoing pattern of saccades. Saccades were made sequentially along a color-cued path. Attention was assessed by a visual memory task presented during a random pause between successive saccades. Saccadic planning had several effects on memory: (1) fewer letters were remembered during intersaccadic pauses than during maintained fixation; (2) letters appearing on the saccadic path, including locations previously examined, could be remembered; off-path performance was near chance; (3) memory was better at the saccadic target than all other locations, including the currently fixated location. These results show that the distribution of attention during intersaccadic pauses results from a combination of top-down enhancement at the saccadic target coupled with a more automatic allocation of attention to selected display locations. This suggests that the visual system has mechanisms to control the distribution of attention without interfering with ongoing saccadic programming.