Contextual coherence increases perceived numerosity independent of semantic content.

Number perception emerges from multiple stages of visual processing. Understanding how systematic biases in number perception occur within a hierarchy of increasingly complex feature representations helps uncover the multistage processing underlying our visual number sense. Recent work demonstrated that reducing coherence of low-level visual attributes, such as color and orientation, systematically reduces perceived number. Here, we ask when in the visual processing hierarchy coherence affects numerosity perception and specifically whether the coherence effect is exclusive to low-level visual features or instead whether it can be driven by contextual or semantic relationships. We tested adults in an ordinal numerical comparison task with contextual coherence mathematically manipulated using a statistical model of visual object co-occurrence. Across several experiments, we found that arrays with high contextual coherence were perceived as numerically larger than arrays with low contextual coherence. This contextual coherence effect was not attenuated even when we reduced objects to texforms (unrecognizable images that preserve midlevel visual features) or removed semantic content from the images through box scrambling and diffeomorphic warping. Together, these results suggest that visual coherence derived from natural statistics of object co-occurrence systematically alters perceived numerosity at low-level visual processing, even before later stages at which items can be explicitly categorized and identified. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Rational number representation by the approximate number system.

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.

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.

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).

Magnitude shifts spatial attention from left to right in rhesus monkeys as in the human mental number line.

Humans typically represent numbers and quantities along a left-to-right continuum. Early perspectives attributed number-space association to culture; however, recent evidence in newborns and animals challenges this hypothesis. We investigate whether the length of an array of dots influences spatial bias in rhesus macaques. We designed a touch-screen task that required monkeys to remember the location of a target. At test, monkeys maintained high performance with arrays of 2, 4, 6, or 10 dots, regardless of changes in the array's location, spacing, and length. Monkeys remembered better left targets with 2-dot arrays and right targets with 6- or 10-dot arrays. Replacing the 10-dot array with a long bar, yielded more accurate performance with rightward locations, consistent with an underlying left-to-right oriented magnitude code. Our study supports the hypothesis of a spatially oriented mental magnitude line common to humans and animals, countering the idea that this code arises from uniquely human cultural learning.

Attention deficits linked with proclivity to explore while foraging.

All mobile organisms forage for resources, choosing how and when to search for new opportunities by comparing current returns with the average for the environment. In humans, nomadic lifestyles favouring exploration have been associated with genetic mutations implicated in attention deficit hyperactivity disorder (ADHD), inviting the hypothesis that this condition may impact foraging decisions in the general population. Here we tested this pre-registered hypothesis by examining how human participants collected resources in an online foraging task. On every trial, participants chose either to continue to collect rewards from a depleting patch of resources or to replenish the patch. Participants also completed a well-validated ADHD self-report screening assessment at the end of sessions. Participants departed resource patches sooner when travel times between patches were shorter than when they were longer, as predicted by optimal foraging theory. Participants whose scores on the ADHD scale crossed the threshold for a positive screen departed patches significantly sooner than participants who did not meet this criterion. Participants meeting this threshold for ADHD also achieved higher reward rates than individuals who did not. Our findings suggest that ADHD attributes may confer foraging advantages in some environments and invite the possibility that this condition may reflect an adaptation favouring exploration over exploitation.

Neurophysiological signatures of approximate number system acuity in preschoolers.

BACKGROUND: A hallmark of the approximate number system (ANS) is ratio dependence. Previous work identified specific event-related potentials (ERPs) that are modulated by numerical ratio throughout the lifespan. In adults, ERP ratio dependence was correlated with the precision of the numerical judgments with individuals who make more precise judgments showing larger ratio-dependent ERP effects. The current study evaluated if this relationship generalizes to preschoolers. METHOD: ERPs were recorded from 56 4.5 to 5.5-year-olds while they compared the numerosity of two sequentially presented dot arrays. Nonverbal numerical precision, often called ANS acuity, was assessed using a similar behavioral task. RESULTS: Only children with high ANS acuity exhibited a P2p ratio-dependent effect onsetting ∼250 ms after the presentation of the comparison dot array. Furthermore, P2p amplitude positively correlated with ANS acuity across tasks. CONCLUSION: Results demonstrate developmental continuity between preschool years and adulthood in the neural basis of the ANS.

Young Children Intuitively Divide Before They Recognize the Division Symbol.

Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 N = 89, Experiment 2 N = 42) and adults (Experiment 3 N = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.

Increasing entropy reduces perceived numerosity throughout the lifespan.

Numerical illusions may provide a powerful window into the mechanisms that give rise to our visual number sense. Recent research has shown that similarly oriented elements appear more numerous than randomly oriented elements in an array. Here we examine whether the orientation coherence illusion is a more general byproduct of the effect of entropy on numerical information-processing. Participants engaged in an ordinal numerical comparison task where the color entropy of arrays was manipulated. We found that arrays with low color entropy were perceived as more numerous than arrays with high color entropy (Experiments 1 and 2), suggesting that the coherence illusion on numerosity perception is not specific to a particular visual property (e.g., orientation) but instead that the entropy of visual arrays more generally affects numerical processing. In Experiment 3, we explored the developmental trajectory of the color entropy effect in children aged 5 to 17 and found that the strength of the coherence illusion increases into adulthood, raising intriguing questions as to how perceptual experiences influence the progression of this numerosity illusion. We consider a recently proposed resource-rational model as a framework for understanding the entropy effect on numerosity perception under an information-theoretic perspective.

Children perform better on left than right targets in an ordinal task.

Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown. Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.

Relative numerical middle in rhesus monkeys.

Animals show vast numerical competence in tasks that require both ordinal and cardinal numerical representations, but few studies have addressed whether animals can identify the numerical middle in a sequence. Two rhesus monkeys (Macaca mulatta) learned to select the middle dot in a horizontal sequence of three dots on a touchscreen. When subsequently presented with longer sequences composed of 5, 7 or 9 items, monkeys transferred the middle rule. Accuracy decreased as the length of the sequence increased. In a second test, we presented monkeys with asymmetrical sequences composed of nine items, where the numerical and spatial middle were distinct and both monkeys selected the numerical middle over the spatial middle. Our results demonstrate that rhesus macaques can extract an abstract numerical rule to bisect a discrete set of items.

Context-Dependent Modulation of Early Visual Cortical Responses to Numerical and Nonnumerical Magnitudes.

Whether and how the brain encodes discrete numerical magnitude differently from continuous nonnumerical magnitude is hotly debated. In a previous set of studies, we orthogonally varied numerical (numerosity) and nonnumerical (size and spacing) dimensions of dot arrays and demonstrated a strong modulation of early visual evoked potentials (VEPs) by numerosity and not by nonnumerical dimensions. Although very little is known about the brain's response to systematic changes in continuous dimensions of a dot array, some authors intuit that the visual processing stream must be more sensitive to continuous magnitude information than to numerosity. To address this possibility, we measured VEPs of participants viewing dot arrays that changed exclusively in one nonnumerical magnitude dimension at a time (size or spacing) while holding numerosity constant and compared this to a condition where numerosity was changed while holding size and spacing constant. We found reliable but small neural sensitivity to exclusive changes in size and spacing; however, exclusively changing numerosity elicited a much more robust modulation of the VEPs. Together with previous work, these findings suggest that sensitivity to magnitude dimensions in early visual cortex is context dependent: The brain is moderately sensitive to changes in size and spacing when numerosity is held constant, but sensitivity to these continuous variables diminishes to a negligible level when numerosity is allowed to vary at the same time. Neurophysiological explanations for the encoding and context dependency of numerical and nonnumerical magnitudes are proposed within the framework of neuronal normalization.

Mental Health and Addiction Response: Supporting Nursing Resilience in a Pandemic.

In their paper, Stelnicki and Carleton (2021) highlight both the findings of their 2019 survey of nurses' mental health (Stelnicki et al. 2020) and more recent literature published during the COVID-19 pandemic. This response outlines the role of nursing leaders in enabling the mental health of nurses in a mental health and addiction setting, particularly during the COVID-19 pandemic.

Approximate multiplication in young children prior to multiplication instruction.

Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can perform a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruction. We presented 5- to 8-year-olds with nonsymbolic multiplicands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a visible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multiplication, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 × 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between children's Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children's emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals.

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

Failure to replicate the benefit of approximate arithmetic training for symbolic arithmetic fluency in adults.

Previous research reported that college students' symbolic addition and subtraction fluency improved after training with non-symbolic, approximate addition and subtraction. These findings were widely interpreted as strong support for the hypothesis that the Approximate Number System (ANS) plays a causal role in symbolic mathematics, and that this relation holds into adulthood. Here we report four experiments that fail to find evidence for this causal relation. Experiment 1 examined whether the approximate arithmetic training effect exists within a shorter training period than originally reported (2 vs 6 days of training). Experiment 2 attempted to replicate and compare the approximate arithmetic training effect to a control training condition matched in working memory load. Experiments 3 and 4 replicated the original approximate arithmetic training experiments with a larger sample size. Across all four experiments (N = 318) approximate arithmetic training was no more effective at improving the arithmetic fluency of adults than training with control tasks. Results call into question any causal relationship between approximate, non-symbolic arithmetic and precise symbolic arithmetic.

Middle identification for rhesus monkeys is influenced by number but not extent.

concept learning provides a fundamental building block for many cognitive functions in humans. Here we address whether rhesus monkeys (Macaca mulatta) can learn the abstract concept of "middle" in a series of objects. First, we trained monkeys to select the middle dot in a horizontal series of three dots presented on a touchscreen. Monkeys maintained a preference to choose the middle dot despite changes in the appearance, location, and spacing of the horizontal series of dots. They maintained high performance when the color, shape and the length of the stimuli were new, indicating that their responses did not depend upon the particular appearance of the array items. Next, we asked whether monkeys would generalize the middle concept to a 7 dot series. Although accuracy decreased when the number of dots was increased, monkeys continued to preferentially select the middle dot. Our results demonstrate that rhesus macaques can learn to use a middle concept for a discrete set of items.

Greenhouse gas emissions from advanced nitrogen-removal onsite wastewater treatment systems.

Advanced onsite wastewater treatment systems (OWTS) designed to remove nitrogen from residential wastewater play an important role in protecting environmental and public health. Nevertheless, the microbial processes involved in treatment produce greenhouse gases (GHGs) that contribute to global climate change, including CO2, CH4, N2O. We measured GHG emissions from 27 advanced N-removal OWTS in the towns of Jamestown and Charlestown, Rhode Island, USA, and assessed differences in flux based on OWTS technology, home occupancy (year-round vs. seasonal), and zone within the system (oxic vs. anoxic/hypoxic). We also investigated the relationship between flux and wastewater properties. Flux values for CO2, CH4, and N2O ranged from -0.44 to 61.8, -0.0029 to 25.3, and -0.02 to 0.23 µmol GHG m-2 s-1, respectively. CO2 and N2O flux varied among technologies, whereas occupancy pattern did not significantly impact any GHG fluxes. CO2 and CH4 - but not N2O - flux was significantly higher in the anoxic/hypoxic zone than in the oxic zone. Greenhouse gas fluxes in the oxic zone were not related to any wastewater properties. CO2 and CH4 flux from the anoxic/hypoxic zone peaked at ~22-23 °C, and was negatively correlated with dissolved oxygen levels, the latter suggesting that CO2 and CH4 flux result primarily from anaerobic respiration. Ammonium concentration and CH4 flux were positively correlated, likely due to inhibition of CH4 oxidation by NH4+. N2O flux in the anoxic/hypoxic zone was not correlated to any wastewater property. We estimate that advanced N-removal OWTS contribute 262 g CO2 equivalents capita-1 day-1, slightly lower than emissions from conventional OWTS. Our results suggest that technology influences CO2 and N2O flux and zone influences CO2 and CH4 flux, while occupancy pattern does not appear to impact GHG flux. Manipulating wastewater properties, such as temperature and dissolved oxygen, may help mitigate GHG emissions from these systems.

Number sense biases children's area judgments.

Humans are thought to use the approximate number system (ANS) to make quick approximations based on quantity even before learning to count. However, there has long been controversy regarding the salience of number versus other stimulus dimensions throughout development, including a recent proposal that number sense is derived from a sense of general magnitude. Here, we used a regression approach to disentangle numerical acuity from sensitivity to total surface area in both 5-year-old children and adults. We found that both children and adults displayed higher acuity when making numerosity judgments than total surface area judgments. Adults were largely able to ignore irrelevant stimulus features when making numerosity or total area judgments. Children were more biased by numerosity when making total area judgments than by total area when making numerosity judgments. These results provide evidence that number is more salient than total surface area even before the start of formal education and are inconsistent with the Sense of Magnitude proposal.

Similarly oriented objects appear more numerous.

Several non-numerical factors influence the numerical estimation of visual arrays, including the spacing of items and whether they are arranged randomly or symmetrically. Here we report a novel numerosity illusion we term the coherence illusion. When items in an array have a coherent orientation (all pointing in the same direction) they seem to be more numerous than when items are oriented randomly. Participants show parametric effects of orientation coherence in three distinct numerical judgment tasks. These findings are not predicted by any current model of numerical estimation. We discuss array entropy as a possible framework for explaining both the coherence illusion and the previously reported regular-random illusion.