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Several empirical approaches have attempted to explain perception of 2D and 3D size. While these approaches have documented interesting perceptual effects, they fail to offer a compelling, general explanation of everyday size perception. Here, we offer one. Building on prior work documenting an ‘Additive Area Heuristic’ by which observers estimate perceived area by summing objects’ dimensions, we show that this same principle — an ‘additive heuristic’ — explains impressions of 3D volume. Observers consistently discriminate sets that vary in ‘additive volume’, even when there is no true difference; they also sometimes fail to discriminate sets that truly differ (even by amounts as much as 200%) when they are equated in ‘additive volume’. However, this heuristic also has limits: when volume varies to large extents, observers may rely on both ‘additive’ and true, mathematical volume to make volume judgments. These results suggest a failure to properly integrate multiple spatial dimensions, and frequent reliance on a perceptual heuristic instead.

Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial–numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgements and/or categorical responses. In the novel “Where was The Number?” task, no explicit numerical judgements were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants’ responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing 2D space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which capture angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments, using a simple visual-matching paradigm, show that (a) representational format is recoverable from the errors that observers make in simple spatial tasks, (b) human-made errors spontaneously favor a polar coordinate system of representation, and (c) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence as well as work on spatial representation at other spatial scales.

People may conceptualize certain categories as held together by a category-specific ‘essence’—some un- observable, critical feature that causes the external features of a category to emerge. Yet there remains an open question about what comprises this essence. Recently, Rose and Nichols have argued that this essence is comprised of tele, or purposes, (and, in turn, that teleology is the internal force that gives rise to external features). However, Neufeld has challenged this work on theoretical grounds, arguing that these effects arise only because people infer an underlying internal change when reasoning about a change in telos. On Neufeld’s view, it is the underlying internal cause, and not the telos itself, that serves as an essence (consistent with classic views of scientific essentialism). Here, we ask: Is teleology the primary force behind psychological essentialism? We begin by successfully replicating Rose and Nichols’ key findings in support of teleological essentialism. In two further experiments, however, we demonstrate that teleology may not the central way that people understand the essences of living things: Internal changes matter at least as much as changes to teleology. These findings suggest that while teleology may be one important cue to category membership and the essences of living things, it may be premature to say that we are ‘teleologically essentialist.’

Adults and children 'promiscuously' endorse teleological answers to 'why' questions-a tendency linked to arguments that humans are intuitively theistic and naturally unscientific. But how do people arrive at an endorsement of a teleological answer? Here, we show that the endorsement of teleological answers need not imply unscientific reasoning (n = 880). A series of experiments show that (a) 'why' questions can be understood as a query for one of two distinct kinds of information and (b) these "implicit questions" can explain adults' answer preferences without appeal to unscientific worldviews. As a strong test of this view, we show that people endorse teleological answers that can answer relevant (implicit) questions about something's purpose, even when those answers are explicitly non-causal. Thus, we argue that endorsement of teleological answers does not necessarily equate to the endorsement of teleological 'explanations': Instead, explanation preferences may simply be an indication of people's pragmatic expectations about the questions that others ask. This view reframes how we should think about explanation preferences in general, while also offering practical insight into the pragmatics of question asking.

Park (2021) has described "flawed stimulus design(s)" in our recent studies on area perception. Here, we briefly respond to those critiques. While the rigorous, computational approaches taken by Park (and others) certainly have value, we believe that our approach - one that focuses the perceptual reality of quantity rather than the physical reality - is essential. We emphasize again (as we have many times in our work) that the study of quantity perception benefits from both approaches. To further illustrate our point, we collected additional data and show that some of Park's arguments, while sensible in principle, further support our view in practice.

A large and growing body of work has documented robust illusions of area perception in adults. To date, however, there has been surprisingly little in-depth investigation into children's area perception, despite the importance of this topic to the study of quantity perception more broadly (and to the many studies that have been devoted to studying children's number perception). Here, in order to understand the interactions of number and area on quantity perception, we study both dimensions in tandem. This work is inspired by recent studies showing that human adults estimate area via an "Additive Area Heuristic," whereby the horizontal and vertical dimensions are summed rather than multiplied. First, we test whether children may rely on this same kind of heuristic. Indeed, "additive area" explains children's area judgments better than true, mathematical area. Second, we show that children's use of "additive area" biases number judgments. Finally, to isolate "additive area" from number, we test children's area perception in a task where number is held constant across all trials. We find something surprising: even when there is no overall effect of "additive area" or "mathematical area," individual children adopt and stick to specific strategies throughout the task. In other words, some children appear to rely on "additive area," while others appear to rely on true, mathematical area - a pattern of results that may be best explained by a misunderstanding about the concept of cumulative area. We discuss how these findings raise both theoretical and practical challenges of studying quantity perception in young children.

Much work has investigated explanatory preferences for things like animals and artifacts, but how do explanation preferences manifest in everyday life? Here, we focus on the criminal justice system as a case study. In this domain, outcomes critically depend on how actors in the system (e.g., lawyers, jurors) generate and interpret explanations. We investigate lay preferences for two difference classes of information: information that appeals to opportunistic aspects of a crime (i.e., how the culprit could have committed the crime) vs. motivational aspects of that crime (i.e., the purpose for committing the crime). In two studies, we demonstrate that people prefer ‘motive’ accounts of crimes (analogous to a teleology preference) at different stages of the investigative process. In an additional two studies we demonstrate that these preferences are context-sensitive: namely, we find that ‘motive’ information tends to be more incriminating and less exculpatory. We discuss these findings in light of a broad literature on the cognitive basis of explanatory preferences; specifically, we draw analogy to preferences for teleological vs. mechanistic explanations. We also discuss implications for the criminal justice system.

Spatial information plays an important role in how we remember. In general, there are two (non mutually exclusive) views regarding the role that space plays in memory. One view is that objects overlapping in space interfere with each other in memory. For example, objects presented in the same location (at different points in time) are more frequently confused with one another than objects that are not. Another view is that spatial information can 'bootstrap' other kinds of information. For example, remembering a phone number is easier one can see the arrangement of a keypad. Here, building on both perspectives, we test the hypothesis that task-irrelevant spatial structure (i.e., objects appearing in stable locations over repeated iterations) improves working memory. Across 7 experiments, we demonstrate that (1) irrelevant spatial structure improves memory for sequences of objects; (2) this effect does not depend on long-term spatial associations; (3) this effect is unique to space (as opposed to features like color); and (4) spatial structure can be teased apart from spatial interference, and the former drives memory improvement. We discuss how these findings relate to and challenge 'spatial interference' accounts as well as 'visuospatial bootstrapping'.

How do we determine how much of something is present? A large body of research has investigated the mechanisms and consequences of number estimation, yet surprisingly little work has investigated area estimation. Indeed, area is often treated as a pesky confound in the study of number. Here, we describe the additive-area heuristic, a means of rapidly estimating visual area that results in substantial distortions of perceived area in many contexts, visible even in simple demonstrations. We show that when we controlled for additive area, observers were unable to discriminate on the basis of true area, per se, and that these results could not be explained by other spatial dimensions. These findings reflect a powerful perceptual illusion in their own right but also have implications for other work, namely, that which relies on area controls to support claims about number estimation. We discuss several areas of research potentially affected by these findings.

Representing spatial information is one of our most foundational abilities. Yet in the present work we find that even the simplest possible spatial tasks reveal surprising, systematic misrepresentations of space-such as biases wherein objects are perceived and remembered as being nearer to the centers of their surrounding quadrants. We employed both a placement task (in which observers see two differently sized shapes, one of which has a dot in it, and then must place a second dot in the other shape so that their relative locations are equated) and a matching task (in which observers see two dots, each inside a separate shape, and must simply report whether their relative locations are matched). Some of the resulting biases were shape specific. For example, when dots appeared in a triangle during the placement task, the dots placed by observers were biased away from certain parts of the symmetry axes. But other systematic biases were not shape specific, and seemed instead to reflect differences in the grain of resolution for different regions of space. For example, with both a circle and even a shapeless configuration (with only a central landmark) in the matching task, observers were better at discriminating angular differences (when a dot changed positions around the circle, as opposed to inward/outward changes) in cardinal versus oblique sectors. These data reveal a powerful angular spatial bias, and highlight how the resolution of spatial representation differs for different regions and dimensions of space itself.

When evaluating information, we cannot always rely on what has been presented as truth: Different sources might disagree with each other, and sometimes there may be no underlying truth. Accordingly, we must use other cues to evaluate information—perhaps the most salient of which is consensus. But what counts as consensus? Do we attend only to surface-level indications of consensus, or do we also probe deeper and consider why sources agree? Four experiments demonstrated that individuals evaluate consensus only superficially: Participants were equally confident in conclusions drawn from a true consensus (derived from independent primary sources) and a false consensus (derived from only one primary source). This phenomenon was robust, occurring even immediately after participants explicitly stated that a true consensus was more believable than a false consensus. This illusion of consensus reveals a powerful means by which misinformation may spread.

A representation of shape that is low dimensional and stable across minor disruptions is critical for object recognition. Computer vision research suggests that such a representation can be supported by the medial axis-a computational model for extracting a shape's internal skeleton. However, few studies have shown evidence of medial axis processing in humans, and even fewer have examined how the medial axis is extracted in the presence of disruptive contours. Here, we tested whether human skeletal representations of shape reflect the medial axis transform (MAT), a computation sensitive to all available contours, or a pruned medial axis, which ignores contours that may be considered ''noise.'' Across three experiments, participants (N = 2062) were shown complete, perturbed, or illusory two-dimensional shapes on a tablet computer and were asked to tap the shapes anywhere once. When directly compared with another viable model of shape perception (based on principal axes), participants' collective responses were better fit by the medial axis, and a direct test of boundary avoidance suggested that this result was not likely because of a task-specific cognitive strategy (Experiment 1). Moreover, participants' responses reflected a pruned computation in shapes with small or large internal or external perturbations (Experiment 2) and under conditions of illusory contours (Experiment 3). These findings extend previous work by suggesting that humans extract a relatively stable medial axis of shapes. A relatively stable skeletal representation, reflected by a pruned model, may be well equipped to support real-world shape perception and object recognition.

How do we represent extent in our spatial world? Recent work has shown that even the simplest spatial judgments — estimates of 2D area — present challenges to our visual system. Indeed, area judgments are best accounted for by ‘additive area’ (the sum of objects' dimensions) rather than ‘true area’ (i.e., a pixel count). But is ‘additive area’ itself the right explanation — or might other models better explain the results? Here, we offer two direct and novel demonstrations that ‘additive area’ explains area judgments. First, using stimuli that are simultaneously equated for number and all other confounding dimensions, we show that area judgments are nevertheless explained by ‘additive area’. Next, we show how ‘scaling’ models of area fail to explain even basic illusions of area. By contrasting squares with diamonds (i.e., the same squares, but rotated), we show a robust tendency to perceive the diamonds as having more area — an effect that no other model of area perception would predict. These results not only confirm the fundamental role of ‘additive area’ in judgments of spatial extent, but they highlight the importance of accounting for this dimension in studies of other features (e.g., density, number) in visual perception.

What determines how well people remember images? Most past research has explored properties of the people doing the remembering — such as their age, emotional state, or individual capacity. However, recent work has also characterized memorability — the likelihood of an image being remembered across observers. But what makes some images more memorable than others? Part of the answer must surely involve the meanings of the images, but here we ask whether this is the entire story: is there also purely visual memorability, driven not by semantic content but by perceptual features per se? We isolated visual memorability in an especially direct manner — by eliminating semantic content while retaining many visual properties. We did so by transforming a set of natural scene images using phase scrambling, and then testing memorability for both intact and scrambled images in independent samples. Across several experiments, observers saw sequences of images and responded anytime they saw a repeated image. We found reliable purely visual memorability at the temporal scales of both short-term memory (2–15 s) and longer-term memory (several minutes), and this could not be explained by the extent to which people could generate semantic labels for some scrambled images. Collectively, these results suggest that the memorability of images is a function not only of what they mean, but also of how they look in the first place.

We distinguish between discrete objects and continuous entities in categorization and language, but might we actually see such stimuli differently? Here we report the one-is-more illusion, wherein ‘objecthood’ changes what we perceive in an unexpected way. Across many variations and tasks, observers perceived a single continuous object (e.g. a rectangle) as longer than an equated set of multiple discrete objects (e.g. two shorter rectangles separated by a gap). This illusion is phenomenologically compelling, exceptionally reliable, and it extends beyond space, to time: a single continuous tone is perceived to last longer than an equated set of multiple discrete tones. Previous work has emphasized the importance of objecthood for processes such as attention and visual working memory, but these results typically require careful analyses of subtle effects. In contrast, we provide striking demonstrations of how perceived objecthood changes the perception of other properties in a way that you can readily see (and hear!) with your own eyes (and ears!).