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.

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.

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).

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.

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.

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.

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.

The second number-estimation elbow: Are visual numbers greater than 20 evaluated differently?

Numerosity perception has long been understood to be divided between subitizing and estimation. In a series of three experiments (total N = 113), a new number "elbow" point in the estimation of visual number for numerosities of about 20 dots is confirmed. Below 20, mean estimates are linear with a slope of about 1 and power-function exponents for numerosity estimation approximate unity, though estimate variance increases dramatically above about 6 elements. For numerosities above 20, estimates become increasingly compressed, such that power function exponents are much lower (e.g., 0.7) and are lower still when both ranges are estimated within the same experimental procedure. The experiments described here show that the location of the inflection point appears insensitive to the range of numbers estimated and to differences in density.

Do Explicit Estimates of Angular Declination Become Ungrounded in the Presence of a Ground Plane?

In a series of seven experiments (total N = 220), it is shown that explicit angular declination judgments are influenced by the presence of a ground plane in the background. This is of theoretical importance because it bears on the interpretation of the relationship between angular declination and perceived distance on a ground plane. Explicit estimates of ground distance are consistent with a simple 1.5 gain in the underlying perceived angular declination function. The experiments show that, in general, functions of estimates of perceived angular declination have a slope of 1.5, but that an additional intercept can often be observed as a result of incorporating changes in ground distance into reports of changes in angular declination. By varying the background context, a variety of functions were observed that are consistent with this contamination hypothesis.

Does perceived angular declination contribute to perceived optical slant on level ground?

When one looks at a spot on level ground, the local optical slant (i.e., surface orientation relative to the line of sight) is geometrically equivalent to the angular declination (i.e., sagittal visual direction relative to horizontal). In theory, angular declination provides an unbiased proximal source of information for estimating optical slant on level ground. Two experiments were conducted to investigate whether human visual systems take advantage of this information. An aspect ratio task was used as an implicit measure for assessing perceived optical slant. Participants gave verbal estimates of the perceived aspect ratio of an L-shaped arrangement, formed by three balls on level ground or on slanted surfaces (hills). Gaze direction was held horizontal when viewing the stimuli on hills. Experiment 1 examined two optical slants (22° to 35°) at relatively short viewing distances (3.1 to 11.5 m), while Experiment 2 tested a shallow optical slant (6°) at relatively long viewing distances (5.7 to 17.2 m). No significant difference in perceived aspect ratio was found between the level-ground and the hill conditions in either experiment. These findings suggest that angular declination does not contribute to perceived optical slant on level ground. It seems that the perception of optical slant and of gaze declination are independent, and this may be because the two variables are normally used jointly to determine a higher order perceptual variable-geographical slant.

Differential Angular Expansion in Perceived Direction in Azimuth and Elevation Are Yoked to the Presence of a Perceived Ground Plane.

It has been proposed that perceived angular direction relative to straight-ahead is exaggerated in perception, and that this exaggeration is greater in elevation (or declination) than in azimuth. Prior research has suggested that exaggerations in elevation may be tied to the presence of a visual ground plane, but there have been mixed results across studies using different methods of dissociation. In the present study, virtual environments were used to dissociate visual from gravitational upright while human participants (N = 128) made explicit angular direction judgments relative to straight ahead. Across these experimental manipulations, observers were positioned either upright (Experiments 1A and 1B) or sideways (Experiment 2), so as to additionally dissociate bodily orientation from gravitational orientation. In conditions in which a virtual environment was perceived as containing a level ground plane, large-scale exaggerations consistent with the visually-specified orientation of the ground plane were observed. In the absence of the perception of a level ground plane, angular exaggerations were relatively small. The ground plane serves as an important reference frame for angular expansion in the perceived visual direction.

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.

A large-scale horizontal-vertical illusion produced with small objects separated in depth.

We conducted two experiments (total N = 81) to investigate the basis for the large-scale horizontal-vertical illusion (HVI), which is typically measured as 15%-20% and has previously been linked to the presence of a ground plane. In a preliminary experiment, vertical rods of similar angular extents that were either large (4.5-7.5 m) and far, or small (0.9-1.5 m) and near, were matched to horizontal extents in a virtual environment by adjustment of horizontal gaps or rods. Large/far objects showed a larger HVI (∼13%) than did small objects (∼7%), as has been shown before, but the horizontal gap normally used to measure the large-scale HVI was not the source of the larger bias. In the second experiment, we found that simply separating the comparison rod in depth from the vertical rod (thus forcing an evaluation of size at a distance) was sufficient to produce a large HVI (17%), even with small rods. The results are interpreted in light of evidence that the large-scale HVI is dependent on ground plane orientation and may be related to differential angular expansion in the visual coding of elevation and azimuth. (PsycINFO Database Record

Counterpoint.

Claims about alterations in perception based on manipulations of the energetics hypothesis (and other influences) are often framed as interesting specifically because they affect our perceptual experience. Many control experiments conducted on such perceptual effects suggest, however, that they are the result of attribution effects and other kinds of judgmental biases influencing the reporting process rather than perception itself. Schnall (2017, this issue), appealing to Heider's work on attribution, argues that it is fruitless to try to distinguish between perception and attribution. This makes the energetics hypothesis less interesting.

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.

Do Individual Differences and Aging Effects in the Estimation of Geographical Slant Reflect Cognitive or Perceptual Effects?

Several individual differences including age have been suggested to affect the perception of slant. A cross-sectional study of outdoor hill estimation (N = 106) was analyzed using individual difference measures of age, experiential knowledge, fitness, personality traits, and sex. Of particular note, it was found that for participants who reported any experiential knowledge about slant, estimates decreased (i.e., became more accurate) as conscientiousness increased, suggesting that more conscientious individuals were more deliberate about taking their experiential knowledge (rather than perception) into account. Effects of fitness were limited to those without experiential knowledge, suggesting that they, too, may be cognitive rather than perceptual. The observed effects of age, which tended to produce lower, more accurate estimates of hill slant, provide more evidence that older adults do not see hills as steeper. The main effect of age was to lower slant estimates; such effects may be due to implicit experiential knowledge acquired over a lifetime. The results indicate the impact of cognitive, rather than perceptual factors on individual differences in slant estimation.

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.

Large perceptual distortions of locomotor action space occur in ground-based coordinates: Angular expansion and the large-scale horizontal-vertical illusion.

What is the natural reference frame for seeing large-scale spatial scenes in locomotor action space? Prior studies indicate an asymmetric angular expansion in perceived direction in large-scale environments: Angular elevation relative to the horizon is perceptually exaggerated by a factor of 1.5, whereas azimuthal direction is exaggerated by a factor of about 1.25. Here participants made angular and spatial judgments when upright or on their sides to dissociate egocentric from allocentric reference frames. In Experiment 1, it was found that body orientation did not affect the magnitude of the up-down exaggeration of direction, suggesting that the relevant orientation reference frame for this directional bias is allocentric rather than egocentric. In Experiment 2, the comparison of large-scale horizontal and vertical extents was somewhat affected by viewer orientation, but only to the extent necessitated by the classic (5%) horizontal-vertical illusion (HVI) that is known to be retinotopic. Large-scale vertical extents continued to appear much larger than horizontal ground extents when observers lay sideways. When the visual world was reoriented in Experiment 3, the bias remained tied to the ground-based allocentric reference frame. The allocentric HVI is quantitatively consistent with differential angular exaggerations previously measured for elevation and azimuth in locomotor space. (PsycINFO Database Record

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.

Manual anchoring biases in slant estimation affect matches even for near surfaces.

People verbally overestimate hill slant by ~15°-25°, whereas manual estimates (e.g., palm board measures) are thought to be more accurate. The relative accuracy of palm boards has contributed to the widely cited theoretical claim that they tap into an accurate, but unconscious, motor representation of locomotor space. Recently, it was shown that a bias that stems from anchoring the hand at horizontal prior to the estimate can quantitatively account for the difference between manual and verbal estimates of hill slant. The present work extends this observation to manual estimates of near-surface slant, to test whether the bias derives from manual or visual uncertainty. As with far surfaces, strong manual anchoring effects were obtained for a large range of near-surface slants, including 45°. Moreover, correlations between participants' manual and verbal estimates further support the conclusion that both measures are based on the same visual representation.