Relative numerosity is constructed from size and density information: Evidence from adaptation.

To dissociate aftereffects of size and density in the perception of relative numerosity, large or small adapter sizes were crossed with high or low adapter densities. A total of 48 participants were included in this preregistered design. To adapt the same retinotopic region as the large adapters, the small adapters were flashed in a sequence so as to "paint" the adapting density across the large region. Perceived numerosities and sizes in the adapted region were then compared to those in an unadapted region in separate blocks of trials, so that changes in density could be inferred. These density changes were found to be bidirectional and roughly symmetric, whereas the aftereffects of size and number were not symmetric. A simple account of these findings is that local adaptations to retinotopic density as well as global adaptations to size combine in producing numerosity aftereffects measured by assessing perceived relative number. Accounts based on number adaptation are contraindicated, in particular, by the result of adapting to a large, sparse adapter and testing with a stimulus with a double the density but half number of dots.

Implied occlusion and subset underestimation contribute to the weak-outnumber-strong numerosity illusion.

Four experimental studies are reported using a total of 712 participants to investigate the basis of a recently reported numerosity illusion called "weak-outnumber-strong" (WOS). In the weak-outnumber-strong illusion, when equal numbers of white and gray dots (e.g., 50 of each) are intermixed against a darker gray background, the gray dots seem much more numerous than the white. Two principles seem to be supported by these new results: 1) Subsets of mixtures are generally underestimated; thus, in mixtures of red and green dots, both sets are underestimated (using a matching task) just as the white dots are in the weak-outnumber-strong illusion, but 2) the gray dots seem to be filled in as if partially occluded by the brighter white dots. This second principle is supported by manipulations of depth perception both by pictorial cues (partial occlusion) and by binocular cues (stereopsis), such that the illusion is abolished when the gray dots are depicted as closer than the white dots, but remains strong when they are depicted as lying behind the white dots. Finally, an online investigation of a prior false-floor hypothesis concerning the effect suggests that manipulations of relative contrast may affect the segmentation process, which produces the visual bias known as subset underestimation.

How frequent is the spontaneous occurrence of synchronized walking in daily life?

Experimental work has suggested that individuals walking side by side may frequently synchronize their steps. The present study created video records of pedestrian activity on pedestrian pathways in order to estimate the frequency of continuous synchronization among pairs of walkers going about their daily lives. About 6% of 498 coded pairs were continuously synchronized. Analysis and modeling of the distributions of frequency differences suggested that while different walkers will tend to have different preferred frequencies for a given speed (i.e., a preferred ratio of step length to step frequency, or walk ratio), they may tend to adjust their walk ratios slightly toward one another's even when they are not synchronizing their steps.

Spatial number estimation has a higher linear range than temporal number estimation; differential affordances for subdivision might help to explain why.

Estimation of visuospatial number typically has a limited linear range that goes well beyond the subitizing range but typically not beyond 20 items without calibration procedures. Three experiments involving a total of 104 undergraduate students, each tested once, sought to determine if the limit on the linear range represented a capacity limitation of a linear accumulator or might be the result of a strategy based on subdividing spatial displays into potentially subitizable subsets. For visual and auditory temporal numbers for a large range of numbers (2-58; Experiment 1), the (unbiased) linear range was found to be quite restricted (three or four items). Using matched linear spatial number stimuli (Experiment 2), the linear range observed extended to about nine or 10 items. Experiment 3 compared estimates when simultaneous two-dimensional spatial number displays were presented briefly, with estimates for identical displays that accumulated over time. The linear range of estimates for accumulating spatial displays reached only 11 items, whereas that for briefly presented displays extended to about 20 items. These results suggest that the limit on the linear range is not simply a capacity limitation in a linear accumulator. Rather, they support the idea that linear spatial number estimation for the range from five to 20 may be based on subdividing the display into a subitizable number of (potentially) subitizable groups, even if those groups are not outwardly marked.

Are subjective ratings of metaphors a red herring? The big two dimensions of metaphoric sentences.

What makes some metaphors easier to understand than others? Several psycholinguistic dimensions have been identified as candidate answers to this question, including appeals to familiarity and aptness. One way to operationalize these dimensions is to collect ratings of them from naive participants. In this article, we question the construct validity of this approach. Do ratings of aptness actually reflect the aptness of the metaphors? Are ratings of aptness measuring something different from ratings of familiarity? With two experiments and an analysis of existing datasets, we argue that ratings of metaphoric sentences are confounded by how easily people are able to understand the sentences (processing fluency). In the experiments, a context manipulation was designed to affect how fluently people would process the metaphors. Experiment 1 confirmed that the manipulation affected how quickly people understood the sentences in a response time task. Experiment 2 revealed that the same manipulation influenced ratings of such dimensions as familiarity and aptness. Finally, factor analyses-on the ratings data from Experiment 2 and from several existing datasets-revealed two underlying sources of variance in sentence-level ratings of metaphors (the "big two" dimensions of metaphoric sentences): processing fluency and figurativeness. We discuss the implications of these findings for theories of figurative-language processing by emphasizing more careful treatment of subjective ratings of metaphoric sentences, and by suggesting the use of alternative methods to manipulate and measure such dimensions as familiarity and aptness.

Multitudes are adaptable magnitudes in the estimation of number.

Visual number comparison does not require participants to choose a unit, whereas units are fundamental to the definition of number. Studies using magnitude estimation rather than comparison show that number perception is compressed dramatically past about 20 units. Even estimates of 5-20 items are increasingly susceptible to effects of visual adaptation, suggesting a rather narrow range in which subitizing-like categorization processes blend into greater reliance on adaptable magnitude information.

Perceived azimuth direction is exaggerated: Converging evidence from explicit and implicit measures.

Recent observations suggest that perceived visual direction in the sagittal plane (angular direction in elevation, both upward and downward from eye level) is exaggerated. Foley, Ribeiro-Filho, and Da Silva's (2004) study of perceived size of exocentric ground extent implies that perceived angular direction in azimuth may also be exaggerated. In the present study, we directly examined whether perceived azimuth direction is overestimated. In Experiment 1, numeric estimates of azimuth direction (-48° to 48° relative to straight ahead) were obtained. The results showed a linear exaggeration in perceived azimuth direction with a gain of about 1.26. In Experiment 2, a perceptual extent-matching task served as an implicit measure of perceived azimuth direction. Participants matched an egocentric distance in one direction to a frontal extent in nearly the opposite direction. The angular biases implied by the matching data well replicated Foley et al.'s finding and were also fairly consistent with the azimuth bias function found in Experiment 1, although a slight overall shift was observed between the results of the two experiments. Experiment 3, in which half the observers were tilted sideways while making frontal/depth extent comparisons, suggested that the discrepancy between the results of Experiment 1 and 2 can partially be explained by a retinal horizontal vertical illusion affecting distance estimation tasks. Overall the present study provides converging evidence to suggest that the perception of azimuth direction is overestimated.

Oh the irony: Perceptual stability is important for action.

I review experiments in which drinking a sugarless drink causes some participants who have low blood sugar from fasting to give lower slant estimates. Ironically, this only occurs to the extent that they believe that they have received sugar and that the sugar was meant to make the hill look shallower; those who received sugar showed no similar effect. These findings support the hypothesis that low blood sugar causes greater participant cooperation - which, in combination with other experimental details, can lead participants to make judgments that can either seem to support the effort hypothesis or contradict it. I also emphasize the importance of perceptual stability in the perception of spatial layout.

Default Reference Frames for Angular Expansion in the Perception of Visual Direction.

Prior work has shown that perceived angular elevation relative to a visible horizon/ground plane is exaggerated with a gain of about 1.5. Here, we investigated whether estimates of angular elevation remain exaggerated when no such visual gravitational reference is provided. This was investigated using a series of five experiments, with most using a novel apparatus to view a large field-of-view stereoscopic virtual environment while lying supine, looking straight up. Magnitude estimation methods were used as well as psychometric matches to internal standards with a total of 133 human participants. Generally, it was found that the exaggerated scaling of elevation seemed to be a default for 3D space, even if testing was performed in virtual environments that were nearly empty. Indeed, for supine observers, a strong exaggeration was found even for azimuthal judgments, which is consistent with the idea that, when looking upward, all deviations are in elevation. This suggests that the overarching gravitational frame often serves as a default reference frame.

Depth compression based on mis-scaling of binocular disparity may contribute to angular expansion in perceived optical slant.

Three studies, involving a total of 145 observers examined quantitative theories of the overestimation of perceived optical slant. The first two studies investigated the depth/width anisotropies on positive and negative slant in both pitch and yaw at 2 and 8 m using calibrated immersive virtual environments. Observers made judgments of the relative lengths of extents that were frontal with those that were in depth. The physical aspect ratio that was perceived as 1:1 was determined for each slant. The observed anisotropies can be modeled by assuming overestimation in perceived slant. Three one-parameter slant perception models (angular expansion, affine depth compression caused by mis-scaling of binocular disparity, and intrinsic bias) were compared. The angular expansion and the affine depth compression models provided significantly better fits to the aspect ratio data than the intrinsic bias model did. The affine model required depth compression at the 2 m distance; however, that was much more than the depth compression measured directly in the third study using the same apparatus. The present results suggest that depth compression based on mis-scaling of binocular disparity may contribute to slant overestimation, especially as viewing distance increases, but also suggest that a functional rather than mechanistic account may be more appropriate for explaining biases in perceived slant in near space.

Perceptual experience as a bridge between the retina and a bicoded cognitive map.

The bicoded cognitive maps described by Jeffery et al. are compared to metric perceptual representations. Systematic biases in perceptual experience of egocentric distance, height, and surface orientation may reflect information processing choices to retain information critical for immediate action (Durgin et al. 2010a). Different information processing goals (route planning vs. immediate action) require different metric information.

Is the approximate number system capacity limited? Extended display duration does not increase the limits of linear number estimation.

The approximate number system (ANS) is widely regarded as handling numbers beyond the subitizing range. However, a review of a variety of historical data suggests there is a sharp break in the estimation of visuospatial number at about 20 items. Estimates below 20 tend to be unbiased. Those above 20 tend to show underestimation that can be well-fit by a power function with an exponent less than one. Here we manipulate display duration between subjects to confirm that this break is not simply an artifact of brief displays, but seems to reflect a shift in perceptual magnitude estimation from an ANS (unbiased estimation) to a correlated numerosity system (with log scaling). Detailed analysis of both response time and variability suggests that the sharp break at 20 observed here may reflect a capacity limitation in a linear accumulator system, which gives way to alternative magnitude information beyond 20. Implications for studies of number comparison and math performance are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Perceptual scale expansion: A natural design for improving the precision of motor control.

Space perception is systematically biased. Few theories of spatial bias address the possible functional advantages of mechanisms that produce spatial biases. The scale expansion hypothesis proposes that many spatial biases are due to the perceptual expansion of visual angles, which acts somewhat like a natural magnifying glass in vision. The present study examined the idea that visual expansion may improve motor precision (i.e., reduce motor variability) in movements when using closed-loop control but not when using open-loop control. Experiment 1 tested this idea in an online tracking task (closed-loop control), whereas Experiment 2 tested it in a fast-hitting task (open-loop control). The results were consistent with the hypothesis. To rule out the effect of the task difference (i.e., tracking vs fast hitting), Experiment 3 examined the effect of visual expansion on the variability of motor performance in a line-reproduction task. The control type (closed-loop or open-loop) was manipulated by the form of visual feedback (online or offline). The results were again consistent with the present assumption. Taken together, the present data suggest that perceptual expansion in vision improves motor-control precision when using closed-loop control (but not when using open-loop control), which supports the scale expansion hypothesis. In addition, the present findings also improve our understanding of how visual error amplification affects motor control.

Manual matching of perceived surface orientation is affected by arm posture: evidence of calibration between proprioception and visual experience in near space.

Proprioception of hand orientation (orientation production using the hand) is compared with manual matching of visual orientation (visual surface matching using the hand) in two experiments. In experiment 1, using self-selected arm postures, the proportions of wrist and elbow flexion spontaneously used to orient the pitch of the hand (20 and 80%, respectively) are relatively similar across both manual matching tasks and manual orientation production tasks for most participants. Proprioceptive error closely matched perceptual biases previously reported for visual orientation perception, suggesting calibration of proprioception to visual biases. A minority of participants, who attempted to use primarily wrist flexion while holding the forearm horizontal, performed poorly at the manual matching task, consistent with proprioceptive error caused by biomechanical constraints of their self-selected posture. In experiment 2, postural choices were constrained to primarily wrist or elbow flexion without imposing biomechanical constraints (using a raised forearm). Identical relative offsets were found between the two constraint groups in manual matching and manual orientation production. The results support two claims: (1) manual orientation matching to visual surfaces is based on manual proprioception and (2) calibration between visual and proprioceptive experiences guarantees relatively accurate manual matching for surfaces within reach, despite systematic visual biases in perceived surface orientation.

On intersectionality: visualizing the invisibility of Black women.

Intersectionality refers to the simultaneous and interacting effects of multiple group categorization on individuals with minoritized status, often leading to being perceived in a manner inconsistent with the additive contributions of those categories. For Black women, a number of findings have contributed to the idea that Black women have a unique perceived absence of status, for example, and are perceived as distinct from being Black or a woman. We sought to quantify and visualize the combined effects of race and gender on judgments of persons using data-defined dimensions (the Semantic Differential; Osgood et al. in The measurement of meaning, University of Illinois Press, Champaign, 1957). Our data suggest that gender and race contribute to orthogonal dimensions of difference in the perception of persons. Whereas white males, white females, and Black males all seem to be perceived in accord with additive effects in these two dimensions, Black females seem to be perceived more neutrally, as if neither their gender nor their race is treated as predictive.

The perception of 2D orientation is categorically biased.

Three experimental paradigms were used to investigate the perception of orientation relative to internal categorical standards of vertical and horizontal. In Experiment 1, magnitude estimation of orientation (in degrees) relative to vertical and horizontal replicated a previously reported spatial orientation bias also measured using verbal report: Orientations appear farther from horizontal than they are, whether numeric judgments are made relative to vertical or to horizontal. Analyses of verbal response patterns, however, suggested that verbal reports underestimate the true spatial bias. A non-verbal orientation bisection task (Experiment 2) confirmed that spatial errors are not due to numeric coding and are larger than the 6° error replicated using verbal methods. A spatial error of 8.6° was found in the bisection task, such that an orientation of about 36.4° from horizontal appears equidistant from vertical and horizontal. Finally, using a categorization ("ABX") paradigm in Experiment 3, it was found that there is less memory confusability for orientations near horizontal than for orientations near vertical. Thus, three different types of measures, two of them non-verbal, provide converging evidence that the coding of orientation relative to the internal standards of horizontal and vertical is asymmetrically biased and that horizontal appears to be the privileged axis.

Adaptation to conflicting visual and physical heading directions during walking.

We investigated the role of global optic flow for visual-motor adaptation of walking direction. In an immersive virtual environment, observers walked to a circular target lying on either a homogeneous ground plane (target-motion condition) or a textured ground plane (ground-flow condition). During adaptation trials, we changed the mapping from physical to visual space to create a conflict between physical and visual heading directions. On these trials, the visual heading specified by optic flow deviated from an observer's physical heading by ±10°. This conflict was not noticed by observers but caused them to walk along curved paths to the target. Over the course of 20 adaptation trials, observers adapted to partially compensate for the conflicts, resulting in straighter paths. When the conflicts were removed post-adaptation, observers showed aftereffects in the opposite direction. The amount of adaptation was similar for target-motion and ground-flow conditions (20-25%), with the ground-flow environment producing slightly faster adaptation and larger aftereffects. We conclude that the visual-motor system can rapidly recalibrate the mapping from physical to visual heading and that this adaptation does not strongly depend on full-field optic flow.

Design, data, and theory regarding a digital hand inclinometer: a portable device for studying slant perception.

Palm boards are often used as a nonverbal measure in human slant perception studies. It was recently found that palm boards are biased and relatively insensitive measures, and that an unrestricted hand gesture provides a more sensitive response (Durgin, Hajnal, Li, Tonge, & Stigliani, Acta Psychologica, 134, 182-197, 2010a). In this article, we describe an original design for a portable lightweight digital device for measuring hand orientation. This device is microcontroller-based and uses a micro inclinometer chip as its inclination sensor. The parts are fairly inexpensive. This device, used to measure hand orientation, provides a sensitive nonverbal method for studying slant perception, which can be used in both indoor and outdoor environments. We present data comparing the use of a free hand to palm-board and verbal measures for surfaces within reach and explain how to interpret free-hand measures for outdoor hills.

Perceived slant of binocularly viewed large-scale surfaces: a common model from explicit and implicit measures.

It is known that the perceived slants of large distal surfaces, such as hills, are exaggerated and that the exaggeration increases with distance. In a series of two experiments, we parametrically investigated the effect of viewing distance and slant on perceived slant using a high-fidelity virtual environment. An explicit numerical estimation method and an implicit aspect-ratio approach were separately used to assess the perceived optical slant of simulated large-scale surfaces with different slants and viewing distances while gaze direction was fixed. The results showed that perceived optical slant increased logarithmically with viewing distance and the increase was proportionally greater for shallow slants. At each viewing distance, perceived optical slant could be approximately fit by linear functions of actual slant that were parallel across distances. These linear functions demonstrated a fairly constant gain of about 1.5 and an intercept that increased logarithmically with distance. A comprehensive three-parameter model based on the present data provides a good fit to a number of previous empirical observations measured in real environments.

Controlled interaction: strategies for using virtual reality to study perception.

Immersive virtual reality systems employing head-mounted displays offer great promise for the investigation of perception and action, but there are well-documented limitations to most virtual reality systems. In the present article, we suggest strategies for studying perception/action interactions that try to depend on both scale-invariant metrics (such as power function exponents) and careful consideration of the requirements of the interactions under investigation. New data concerning the effect of pincushion distortion on the perception of surface orientation are presented, as well as data documenting the perception of dynamic distortions associated with head movements with uncorrected optics. A review of several successful uses of virtual reality to study the interaction of perception and action emphasizes scale-free analysis strategies that can achieve theoretical goals while minimizing assumptions about the accuracy of virtual simulations.