Do children estimate area using an "Additive-Area Heuristic"?

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.

The Shape of Space: Evidence for Spontaneous but Flexible Use of Polar Coordinates in Visuospatial Representations.

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.

A Ubiquitous Illusion of Volume: Are Impressions of 3D Volume Captured by an "Additive Heuristic"?

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 fail to discriminate sets that truly differ (even by amounts as much as 30%) when they are equated in "additive volume." These results suggest a failure to properly integrate multiple spatial dimensions, and frequent reliance on a perceptual heuristic instead.

Numerosity, area-osity, object-osity? Oh my.

There is ongoing debate about whether number is perceived directly. Clarke and Beck suggest that what plagues this debate is a lack of shared understanding about what it means to perceive number in the first place. I agree. I argue that the perception of number is held to a different standard than, say, the perception of objecthood; considering this, I explore what it might mean for the number system to represent rational numbers.

The Additive-Area Heuristic: An Efficient but Illusory Means of Visual Area Approximation.

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.

The Illusion of Consensus: A Failure to Distinguish Between True and False Consensus.

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.

Skeletal representations of shape in human vision: Evidence for a pruned medial axis model.

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.

Intuitive network topology.

Topology is the branch of mathematics that seeks to understand and describe spatial relations. A number of studies have examined the human perception of topology-in particular, whether adults and young children perceive and differentiate objects based on features like closure, boundedness, and emptiness. Topology is about more than "wholes and holes," however; it also offers an efficient language for representing network structure. Topological maps, common for subway systems across the world, are an example of how effective this language can be. Inspired by this idea, here we examine "intuitive network topology." We first show that people readily differentiate objects based on several different features of topological networks. We then show that people both remember and match objects in accordance with their topology, over and above substantial variation in their surface features. These results demonstrate that humans possess an intuitive understanding for the basic topological features of networks, and hint at the possibility that topology may serve as a format for representing relations in the mind. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Oblique warping: A general distortion of spatial perception.

There are many putatively distinct phenomena related to perception in the oblique regions of space. For instance, the classic oblique effect describes a deficit in visual acuity for oriented lines in the obliques, and classic "prototype effects" reflect a bias to misplace objects towards the oblique regions of space. Yet these effects are explained in very different terms: The oblique effect itself is often understood as arising from orientation-selective neurons, whereas prototype effects are described as arising from categorical biases. Here, we explore the possibility that these effects (and others) may stem from a single underlying spatial distortion. We show that there is a general distortion of (angular) space in the oblique regions that influences not only orientation judgments, but also location, extent, and size. We argue that these findings reflect oblique warping, a general distortion of spatial representations in the oblique regions which may be the root cause of many oblique effects.

Number adaptation: A critical look.

It is often assumed that adaptation - a temporary change in sensitivity to a perceptual dimension following exposure to that dimension - is a litmus test for what is and is not a "primary visual attribute". Thus, papers purporting to find evidence of number adaptation motivate a claim of great significance: That number is something that can be seen in much the way that canonical visual features, like color, contrast, size, and speed, can. Fifteen years after its reported discovery, number adaptation's existence seems to be nearly undisputed, with dozens of papers documenting support for the phenomenon. The aim of this paper is to offer a counterweight - to critically assess the evidence for and against number adaptation. After surveying the many reasons for thinking that number adaptation exists, we introduce several lesser-known reasons to be skeptical. We then advance an alternative account - the old news hypothesis - which can accommodate previously published findings while explaining various (otherwise unexplained) anomalies in the existing literature. Next, we describe the results of eight pre-registered experiments which pit our novel old news hypothesis against the received number adaptation hypothesis. Collectively, the results of these experiments undermine the number adaptation hypothesis on several fronts, whilst consistently supporting the old news hypothesis. More broadly our work raises questions about the status of adaptation itself as a means of discerning what is and is not a visual attribute.

Event representation at the scale of ordinary experience.

Weeks are divided into weekdays and weekends; years into semesters and seasons; lives into stages like childhood, adulthood, and adolescence. How does the structure of experience shape memory? Though much work has examined event representation in human cognition, little work has explored event representation at the scale of ordinary experience. Here, we use shared experiences - in the form of popular television shows - to explore how memories are shaped by event structure at a large scale. We find that memories for events in these shows exhibit several hallmarks of event cognition. Namely, we find that memories are organized with respect to their event structure (boundaries), and that beginnings and endings are better remembered at multiple levels of the event hierarchy simultaneously. These patterns seem to be partially, but not fully, explained by the perceived story-relevance of events. Lastly, using a longitudinal design, we also show how event representations evolve over periods of several months. These results offer an understanding of event cognition at the scale of ordinary human lives.

A common format for representing spatial location in visual and motor working memory.

Does the mind rely on similar systems of spatial representation for both perception and action? Here, we assessed the format of location representations in two simple spatial localization tasks. In one task, participants simply remembered the location of an item based solely on visual input. In another, participants remembered the location of a point in space based solely on kinesthetic input. Participants' recall errors were more consistent with the use of polar coordinates than Cartesian coordinates in both tasks. Moreover, measures of spatial bias and performance were correlated across modalities. In a subsequent study, we tested the flexibility with which people use polar coordinates to represent space; we show that the format in which the information is presented to participants influences how that information is encoded and the errors that are made as a result. We suggest that polar coordinates may be a common means of representing location information across visual and motor modalities, but that these representations are also flexible in form.

More than a moment: What does it mean to call something an 'event'?

Experiences are stored in the mind as discrete mental units, or 'events,' which influence-and are influenced by-attention, learning, and memory. In this way, the notion of an 'event' is foundational to cognitive science. However, despite tremendous progress in understanding the behavioral and neural signatures of events, there is no agreed-upon definition of an event. Here, we discuss different theoretical frameworks of event perception and memory, noting what they can and cannot account for in the literature. We then highlight key aspects of events that we believe should be accounted for in theories of event processing--in particular, we argue that the structure and substance of events should be better reflected in our theories and paradigms. Finally, we discuss empirical gaps in the event cognition literature and what the future of event cognition research may look like.

Redundancy and Reducibility in the Formats of Spatial Representations.

Mental representations are the essence of cognition. Yet to understand how the mind works, one must understand not just the content of mental representations (i.e., what information is stored) but also the format of those representations (i.e., how that information is stored). But what does it mean for representations to be formatted? How many formats are there? Is it possible that the mind represents some pieces of information in multiple formats at once? To address these questions, I discuss a "case study" of representational format: the representation of spatial location. I review work (a) across species and across development, (b) across spatial scales, and (c) across levels of analysis (e.g., high-level cognitive format vs. low-level neural format). Along the way, I discuss the possibility that the same information may be organized in multiple formats simultaneously (e.g., that locations may be represented in both Cartesian and polar coordinates). Ultimately, I argue that seemingly "redundant" formats may support the flexible spatial behavior observed in humans and that researchers should approach the study of all mental representations with this possibility in mind.

Are we Teleologically Essentialist?

People may conceptualize certain categories as held together by a category-specific "essence"-some unobservable, critical feature that causes the external features of a category to emerge. But what is the nature of this essence? Recently, Rose and Nichols have argued that something's essence is fundamentally its telos or purpose. 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. In 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 be the central way that people understand the essences of living things. We show that internal changes matter at least as much as changes in 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."

Understanding "Why:" How Implicit Questions Shape Explanation Preferences.

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.

Quantity perception: The forest and the trees.

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.

Says who? Children consider informants' sources when deciding whom to believe.

To successfully navigate the world, we cannot simply accept everything we hear as true. We must think critically about others' testimony, believing only sources who are well-informed and trustworthy. This ability is especially crucial in early childhood, a time when we both learn the most, and have the least prior knowledge we can fall back upon to verify others' claims. While even young children evaluate testimony by considering whether agents' firsthand experiences license their claims, much of the time, our informants do not possess firsthand knowledge. When agents transmit information learned from others (rather than discovered firsthand), can children also evaluate their testimony's social basis? Across 3 experiments (N = 390), we manipulate the number of primary sources originating a claim, and the number of secondary sources repeating it. We find that by age 6, children understand that a claim is only as reliable as its original source, endorsing claims supported by more primary (rather than secondary) sources. While young preschoolers already understand the link between firsthand perceptual access and knowledge, these results suggest that a full understanding of testimony's social basis may be later-developing. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

How We See Area and Why It Matters.

A large and growing literature examines how we see the visual quantities of number, area, and density. The literature rests on an untested assumption: that our perception of area is veridical. Here, we discuss a systematic distortion of perceived area and its implications for quantity perception more broadly.

Spatial-numerical associations from a novel paradigm support the mental number line account.

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.