Search

While domestic horses can be trained to choose the highest numerosity, spontaneous choice tests led to contrasting results, which in part might have depended upon the adopted experimental protocols. To bring further evidence, we carried out two experiments based on binary choice tests (1:4, 1:2, 2:3, 4:6 apple halves). We tested both horses used for schooling (N = 25) and semi-wild bred horses (N = 10), using two different arenas. In both experiments, horses did not choose the highest quantity, irrespective of test difficulty. Horses preferentially chose the stimulus located at their left, while no other tested variable affected their choice. The consistency between the results suggests that the lack of discrimination did not depend on test protocols. The strong preference for a given side and high within-individual repeatability indicate that lateralization may affect the results of spontaneous tests. [ABSTRACT FROM AUTHOR]

Despite their young age, zebrafish larvae have a well-developed visual system and can distinguish between different visual stimuli. First, we investigated if the first visual surroundings the larvae experience during the first days after hatching shape their habitat preference. Indeed, these animals seem to "imprint" on the first surroundings they see and select visual stimuli accordingly at 7 days post fertilization (dpf). In particular, if zebrafish larvae experience a bar background just after hatching, they later on prefer bars over white stimuli, and vice versa. We then used this acquired preference for bars to investigate innate numerical abilities. We wanted to specifically test if the zebrafish larvae show real numerical abilities or if they rely on a lower-level mechanism—i.e. spatial frequency—to discriminate between two different numerosities. When we matched the spatial frequency in stimuli with different numbers of bars, the larvae reliably selected the higher numerosity. A previous study has ruled out that 7 dpf zebrafish larvae use convex hull, cumulative surface area and density to choose between two numerosities. Therefore, our results indicate that zebrafish larvae rely on real numerical abilities rather than other cues, including spatial frequency, when spontaneously comparing two sets with different numbers of bars. [ABSTRACT FROM AUTHOR]

Vittorio Benussi (1878–1927) is known for numerous studies on optical illusions, visual and haptic perception, spatial and time perception. In Padova, he had a brilliant student who carefully worked on the topic of how people estimate numerosity, Silvia De Marchi (1897–1936). Her writings have never been translated into English before. Here we comment on her work and life, characterized also by the challenges faced by women in academia. The studies on perception of numerosity from her thesis were published as an article in 1929. We provide a translation from Italian, a redrawing of its 23 illustrations and of the graphs. It shows an original experimental approach and an anticipation of what later became known as magnitude estimation. [ABSTRACT FROM AUTHOR]

Our everyday perceptual experiences are grounded in the integration of information within and across our senses. Due to this direct behavioural relevance, cross‐modal integration retains a certain degree of contextual flexibility, even to social relevance. However, how social relevance modulates cross‐modal integration remains unclear. To investigate possible mechanisms, Experiment 1 tested the principles of audio‐visual integration for numerosity estimation by deriving a Bayesian optimal observer model with perceptual prior from empirical data to explain perceptual biases. Such perceptual priors may shift towards locations of high salience in the stimulus space. Our results showed that the tendency to over‐ or underestimate numerosity, expressed in the frequency and strength of fission and fusion illusions, depended on the actual event numerosity. Experiment 2 replicated the effects of social relevance on multisensory integration from Scheller & Sui, 2022 JEP:HPP, using a lower number of events, thereby favouring the opposite illusion through enhanced influences of the prior. In line with the idea that the self acts like a prior, the more frequently observed illusion (more malleable to prior influences) was modulated by self‐relevance. Our findings suggest that the self can influence perception by acting like a prior in cue integration, biasing perceptual estimates towards areas of high self‐relevance. [ABSTRACT FROM AUTHOR]

Introduction: Associating multimodal information is essential for human cognitive abilities including mathematical skills. Multimodal learning has also attracted attention in the field of machine learning, and it has been suggested that the acquisition of better latent representation plays an important role in enhancing task performance. This study aimed to explore the impact of multimodal learning on representation, and to understand the relationship between multimodal representation and the development of mathematical skills. Methods: We employed a multimodal deep neural network as the computational model for multimodal associations in the brain. We compared the representations of numerical information, that is, handwritten digits and images containing a variable number of geometric figures learned through single- and multimodal methods. Next, we evaluated whether these representations were beneficial for downstream arithmetic tasks. Results: Multimodal training produced better latent representation in terms of clustering quality, which is consistent with previous findings on multimodal learning in deep neural networks. Moreover, the representations learned using multimodal information exhibited superior performance in arithmetic tasks. Discussion: Our novel findings experimentally demonstrate that changes in acquired latent representations through multimodal association learning are directly related to cognitive functions, including mathematical skills. This supports the possibility that multimodal learning using deep neural network models may offer novel insights into higher cognitive functions. [ABSTRACT FROM AUTHOR]

Everyday experiences suggest that a container, such as a box of cereal, can convey pertinent information about the nature and quantity of its content. This study investigated how well people can judge large quantities of objects in a container through haptic perception. Stimuli consisted of plastic drinking straws cut to "small" (1.5 cm) or "big" (4.5 cm) pieces contained in plastic food containers. Participants performed both a magnitude estimation of the number of objects and a direct estimation of the proportion of the container perceived to be filled with objects. Overall, participants demonstrated considerable accuracy for both tasks and irrespective of the size of the content. Post-experiment interviews revealed three potential strategies. Participants either focused on the container's contents, the excess space in the container, or the perceived weight of the container (content). [ABSTRACT FROM AUTHOR]

Copyright of Canadian Journal of Administrative Sciences (John Wiley & Sons, Inc.) is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Everyday experiences suggest that a container, such as a box of chocolate sprinkles, can convey pertinent information about the nature of its content. Despite the familiarity of the experience, we do not know whether people can perceive the number of objects in the container from touch alone and how accurately they can do so. In three experiments, participants handled containers holding between one and five objects and verbally estimated their number. Containers were small cardboard jewelry boxes, and objects were round beads of varying diameter and weight. Any useful visual and auditory cues were precluded. Experiment 1 demonstrated very accurate performance, provided the objects were of sufficient weight. Experiment 2 demonstrated that withholding information about the possible number of objects inside the container does not affect accuracy at a group level but does produce occasional overestimations at an individual level. Experiment 3 demonstrated that removing the weight cue leads to systematic underestimations but does not eliminate people's ability to distinguish between different numbers of objects in the container. This study contributes to a growing picture that container haptics is surprisingly capable. [ABSTRACT FROM AUTHOR]

There are many situations in which we interact with collections of objects, from a crowd of people to a bowl of blackberries. There is an experience of the quantity of these items, although not a precise number, and we have this impression quickly and effortlessly. It can be described as an expressive property of the whole. In the literature, the study of this sense of numerosity has a long history, which is reviewed here with examples. I argue that numerosity is a direct perceptual experience, and that all experiences of numerosity, not only estimations, are affected by perceptual organisation. [ABSTRACT FROM AUTHOR]

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely respected hypotheses that explain cardinality-principle development as building on young learners' ability to subitize small numbers. These hypotheses consider subitizing to be the basis of cardinality-principle development. We argue that there is a qualitative and significant difference between subitizing and the cardinality principle and that the explanation provided are insufficient to account for a change of this magnitude. We then propose a conjecture intended to better explain this change. The conjecture describes counting as the medium for a series of reflective abstractions leading to the cardinality principle. [ABSTRACT FROM AUTHOR]

Ponzo is a familiar name in psychology because of the illusion that takes his name. He had a long and productive career in Italy, and some of his work was translated for international journals already in his lifetime. However, few of these papers are available in English. We provide a commentary that considers how his name came to be associated with an illusion he did not discover. We explain the content of several papers, some of which are often cited in a wrong context in the literature (i.e., papers on touch mentioned in relation to the Ponzo illusion). More importantly, we discuss his contribution to the study of perceived numerosity, and provide a full translation of his important 1928 paper, including a redrawing of its 28 illustrations. [ABSTRACT FROM AUTHOR]

Both symbolic (digits) and non-symbolic (dots) numerals are spatially coded, with relatively small numbers being responded faster with a left key and large numbers being responded faster with a right key (spatial–numerical association of response codes [SNARC]). The idea of format independent SNARC seems to support the existence of a common system for symbolic and non-symbolic numerical representations, although evidence in the field is still mixed. The aim of the present study is to investigate whether symbolic and non-symbolic numerals interact in the SNARC effect when both information is simultaneously displayed. To do so, participants were presented with dice-like patterns, with digits being used instead of dots. In two separate magnitude classification tasks, participants had to respond either to the number of digits presented on the screen or to their numerical size. In the non-symbolic task, they had to judge whether the digits on the screen were more or less than three, irrespective of the numerical value of the digits. In the symbolic task, participants had to judge whether the digits on the screen were numerically smaller or larger than three, irrespective of the number of digits being present. The results show a consistent SNARC effect in the symbolic task and no effect in the non-symbolic one. Furthermore, congruency between symbolic and non-symbolic numerals did not modulate the response patterns, thus supporting the idea of independent representations and questioning some propositions of current theoretical accounts. [ABSTRACT FROM AUTHOR]

This study investigated the perception of numbers in humans in 3D stimuli. Recent research has shown that number processing relies on "number sense" for small values, in line with Weber's law. While previous studies have reported 3D numerosity overestimation mainly in higher numerical values, our experiment examined whether this phenomenon occurs at lower numerical values. We also explored whether the Weber ratio follows Weber's law when comparing 2D and 3D stimuli in terms of the number of elements. Observers were presented with pairs of stimuli on a monitor and were asked to identify the stimulus with a larger number of elements. Using the constant method, we calculated the point of subjective equality (PSE), just noticeable difference (JND), and Weber ratios from the collected data. As a result, it was confirmed that the phenomenon of over-estimation of 3D numerical values occurs even when the numerical values are small. Additionally, we observed that the Weber fraction adhered to Weber's law within the measured range. These findings contribute to the existing body of research, supporting the existence of distinct mechanisms for perceiving numerosity and density. [ABSTRACT FROM AUTHOR]

Discriminating between different quantities is an essential ability in daily life that has been demonstrated in a variety of non-human vertebrates. Nonetheless, what drives the estimation of numerosity is not fully understood, as numerosity intrinsically covaries with several other physical characteristics. There is wide debate as to whether the numerical and spatial abilities of vertebrates are processed by a single magnitude system or two different cognitive systems. Adopting a novel approach, we aimed to investigate this issue by assessing the interaction between area size and numerosity, which has never been conceptualized with consideration for subjective experience in non-human animals. We examined whether the same perceptual biases underlying one of the best-known size illusions, the Delboeuf illusion, can be also identified in numerical estimation tasks. We instructed or trained human participants and guppies, small teleost fish, to select a target numerosity (larger or smaller) of squares between two sets that actually differed in their numerosity. Subjects were also presented with illusory trials in which the same numerosity was presented in two different contexts, against a large and a small background, resembling the Delboeuf illusion. In these trials, both humans and fish demonstrated numerical biases in agreement with the perception of the classical version of the Delboeuf illusion, with the array perceived as larger appearing more numerous. Thus, our results support the hypothesis of a single magnitude system, as perceptual biases that influence spatial decisions seem to affect numerosity judgements in the same way. [ABSTRACT FROM AUTHOR]

Can you reduce uncertainty by thinking? Intuition suggests that this happens through the elusive process of attention: if we expend mental effort, we can increase the reliability of our sensory data. Models based on "rational inattention" formalize this idea in terms of a trade-off between the costs and benefits of attention. This paper surveys the origin of these models in economics, their connection to rate-distortion theory, and some of their recent applications to psychology and neuroscience. We also report new data from a numerosity judgment task in which we manipulate performance incentives. Consistent with rational inattention, people are able to improve performance on this task when incentivized, in part by increasing the reliability of their sensory data. [ABSTRACT FROM AUTHOR]

If you are stuck in a traffic jam, the more numerous the queuing cars are, the longer you expect to wait. Time and numerosity are stimulus dimensions often associated in the same percept and whose interaction can lead to misjudgements. At brain level it is unclear to which extent time and numerosity recruit same/different neural populations and how their perceptual integration leads to changes in these populations' responses. Here we used high-spatial-resolution functional magnetic resonance imaging with neural model-based analyses to investigate how the topographic representations of numerosity and time change when these dimensions are varied together on the same visual stimulus in a congruent (the more numerous the items, the longer the display time) or incongruent manner. Compared to baseline conditions, where only one dimension was changed at a time, the variation of both stimulus dimensions led to changes in neural population responses that became more sensitive either to the two features or to one of them. Magnitude integration led also to degradation of topographies and shifts in response preferences. These changes were more pronounced in the comparison between parietal and frontal maps. Our results while pointing to partially distinct representations of time and numerosity show a common neural response to magnitude integration. [ABSTRACT FROM AUTHOR]

Visual numerosity is represented automatically and rapidly, but much remains unknown about the computations underlying this perceptual experience. For example, it is unclear whether numerosity is represented with an opponent channel or multichannel coding system. Within an opponent channel system, all numerical values are represented via the relative activity of two pools of neurons (i.e., one pool with a preference for small numerical values and one pool with a preference for large numerical values). However, within a multichannel coding system, all numerical values are represented directly, with separate pools of neurons for each (discriminable) numerical value. Using an adaptation paradigm, we assessed whether the visual perception of number is better characterized by an opponent channel or multichannel system. Critically, these systems make distinct predictions regarding the pattern of aftereffects exhibited when an observer is adapted to an intermediate numerical value. Opponent channel coding predicts no aftereffects because both pools of neurons adapt equally. By contrast, multichannel coding predicts repulsive aftereffects, wherein numerical values smaller than the adapter are underestimated and those larger than the adapter are overestimated. Consistent with multichannel coding, visual adaptation to an intermediate value (50 dots) yielded repulsive aftereffects, such that participants underestimated stimuli ranging from 10-50 dots, but overestimated stimuli ranging from 50-250 dots. These findings provide novel evidence that the visual perception of number is supported by a multichannel, not opponent channel, coding system, and raise important questions regarding the contributions of different cortical regions, such as the ventral and lateral intraparietal areas, to the representation of number. [ABSTRACT FROM AUTHOR]

In four experiments we investigated the Solitaire illusion. In this illusion, most observers see as more numerous a set of dots that forms a single central group, compared to dots on the outside of that group. We confirmed and extended the effect to configurations with much higher numerosity than the original and of various colours. Contrary to prediction, separating the two groups, so that they are presented side by side, reduced but did not abolish or reverse the illusion. In this illusion, therefore, neither total size of the region (area), not average distance of the elements has the expected effect. In Experiments 3 and 4 we eliminated the regularity of the pattern, by sampling 50% (Exp 3) or only a 10% (Exp 4) of the elements. These produces quasi‐random configurations. For these configurations the bias for the inner groups was still present, and it was only eliminated when the groups were shown as separate. However, the effect never reversed (no bias for the outer group, despite its larger area). We conclude that the Solitaire illusion is evidence of a strong bias in favour of centrally located elements, a bias that can overcome other factors. [ABSTRACT FROM AUTHOR]

In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into account that there are non-numerical methods of assessing numerosity, which opens up the possibility that cognitive agents lacking numerical abilities may still be able to represent numerosity. In this paper, I distinguish between numerical and non-numerical methods of assessing numerosity and show that the most common models of the internal mechanisms of the so-called number sense rely on non-numerical methods, despite the claims of their proponents to the contrary. I conclude that, even if it is established that agents attend to numerosity, rather than continuous properties of stimuli correlated with it, an answer to the question of the existence of the number sense is still pending the investigation of a further issue, namely, whether the mechanisms the brain uses to assess numerosity qualify as numerical or nonnumerical. [ABSTRACT FROM AUTHOR]

In this study, we investigated the influence of negative emotions on numerosity estimation and whether this influence changes with aging during adulthood. Young and older adults were asked to estimate and compare the numerosity of collections of elements (cars or dots) with a two-digit number. Collections of elements were preceded by emotionally neutral (e.g., mushrooms) or emotionally negative (e.g., a corpse) pictures. Stimuli were easier (i.e., small-ratio) or harder (i.e., large-ratio) items. Young and older participants obtained similar numerosity estimation performance. Interestingly, participants were less accurate under negative emotions than under neutral emotions when they estimated numerosity of collections of abstract elements (i.e., dots). In contrast, participants improved their performance under negative emotions while estimating collections of non-abstract, daily-life elements (i.e., cars). These findings have important implications for furthering our understanding of the role of negative emotions in numerosity estimation and age-related differences therein. [ABSTRACT FROM AUTHOR]

A significant amount of research on numerosity demonstrates that product perceptions are often influenced by the scale on which numerical attribute information is presented. However, fewer studies have examined how self-control is influenced by the numerosity of cost information (e.g. price, nutritional content) in situations that may violate a personal goal. The present research demonstrates that, in such situations, the numerosity of cost information has a stronger influence on self-control when consumers are highly focused on restraint. Because restrained consumers regulate their behavior by anticipating the negative emotions from violating their goals, they experience a narrowing of attention during self-control decisions that makes them more reliant on numerosity as a cue for judgment. The results of eight experiments demonstrate that consumers who are primed or predisposed to be high in restraint display less self-control when cost information is presented on a contracted scale with small numbers compared to an expanded scale with large numbers. When consumers are less focused on restraint, numerosity has less of an effect on self-control because unrestrained consumers do not experience an analogous narrowing of attention. [ABSTRACT FROM AUTHOR]

Consumers typically infer greater quantity from larger numbers. For instance, a 500 gram box of chocolates appears heavier than a.5 kilogram box. By expressing quantities in alternative units or attribute dimensions, one can represent an otherwise identical quantity in a more versus less discretized manner (e.g. a box containing 25 chocolates vs. a box weighing 500 grams). Seven experimental studies show that a difference between more discretized quantities (e.g. 25 vs. 50 chocolates) appears larger relative to a difference between less discretized quantities (e.g. 500 grams vs. 1,000 grams), above and beyond effects of number magnitude. More discretized quantity expressions enhance the consumers' ability to discriminate between choice options and can also nudge consumers to more favorable choices. Because more discretized quantities are more evaluable, expressing a quantity in terms of a collection of elements particularly helps individuals who are less numerically proficient. By identifying how discretization functions as a novel antecedent of evaluability and by distinguishing two different conceptualizations of numerosity (i.e. symbolic and perceptual numerosity), this article draws important connections between the numerical cognition literature and General Evaluability Theory. [ABSTRACT FROM AUTHOR]

In the present study, we investigated the effects of auditory numerosity and magnitude (loudness) on visual numerosity processing. Participants compared numerosities of two sequential dot arrays. The second dot array was paired with a tone array that was independent of visual comparison. The numerosity (One-tone vs. Multiple-tone) and the non-numerical magnitude of tones (loudness) were manipulated in Experiments 1 and 2, respectively. In Experiment 1, participants' inverse efficiency score (IES), that is, the quotient between response time and accuracy, was significantly smaller in the One-tone and Multiple-tone conditions than that in the No-tone condition, and linear trend analyses showed that the IES decreased with the number of tones. In Experiment 2, the IES in the Loud-tone condition was significantly smaller than that in the No-tone condition, and the IES decreased as the loudness of the tones increased. In Experiment 3, both auditory numerosity and magnitude were manipulated. For soft tones, the IES was smaller in the Multiple-tone condition than in the One-tone condition, whereas no significant difference was found between two conditions in loud tones. In sum, these findings suggest that the visual numerical representation can be spontaneously affected by the numerosity and non-numerical magnitude of stimuli from another modality. [ABSTRACT FROM AUTHOR]

The "mental number line" (MNL) is a form of spatial numeric representation that associates small and large numbers with the left and right spaces, respectively. This spatio-numeric organization can be found in adult humans and has been related to cultural factors such as writing and reading habits. Yet, both human newborns and birds order numbers consistently with an MNL, thus raising the question of whether culture is a main explanation for MNL. Here, we explored the numeric sense of honey bees and show that after being trained to associate numbers with a sucrose reward, they order numbers not previously experienced from left to right according to their magnitude. Importantly, the location of a number on that scale varies with the reference number previously trained and does not depend on low-level cues present on numeric stimuli. We provide a series of neural explanations for this effect based on the extensive knowledge accumulated on the neural underpinnings of visual processing in honey bees and conclude that the MNL is a form of numeric representation that is evolutionarily conserved across nervous systems endowed with a sense of number, irrespective of their neural complexity. [ABSTRACT FROM AUTHOR]

In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms 'number,' 'numerosity,' and 'numerousness.' Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a "terminological chaos" in the field of numerical cognition. In this paper, I review Stevens's distinctions to help bring order to this alleged chaos and to shed light on two closely related questions: whether it is adequate to speak of a number sense and how philosophers can make sense of the claim by cognitive scientists that numbers are perceptual entities. Moreover, I offer further support to Stevens's distinction between numerosity and numerousness by showing that they are relational properties that emerge through different relationships between agents and their environments. The final conclusion is that, by adopting Stevens's distinctions, numbers do not need to be seen as perceptual entities, since the so-called number sense is better described as a sense of numerousness. [ABSTRACT FROM AUTHOR]

There is ample evidence from literature and clinical practice indicating mathematical difficulties in individuals with ADHD, even when there is no concomitant diagnosis of developmental dyscalculia. What factors underlie these difficulties is still an open question. Research on dyscalculia and neurotypical development suggests visual perception of numerosity (the number sense) as a building block for math learning. Participants with lower numerosity estimation thresholds (higher precision) are often those with higher math capabilities. Strangely, the role of numerosity perception in math skills in ADHD has been neglected, leaving open the question whether math difficulties in ADHD also originate from a deficitary visual number sense. In the current study we psychophysically measured numerosity thresholds and accuracy in a sample of children/adolescents with ADHD, but not concomitant dyscalculia (N = 20, 8–16 years). Math abilities were also measured by tasks indexing different mathematical competences. Numerosity performance and math scores were then compared to those obtained from an age-matched control group (N = 20). Bayesian statistics indicated no difference between ADHD and controls on numerosity perception, despite many of the symbolic math tasks being impaired in participants with ADHD. Moreover, the math deficits showed by the group with ADHD remained substantial even when numerosity thresholds were statistically regressed out. Overall, these results indicate that math difficulties in ADHD are unlikely to originate from an impaired visual number sense. [ABSTRACT FROM AUTHOR]

Background: Despite the interest and potential of multi touch devices, there are limited published studies researching their effectiveness and usability specifically with children with Down syndrome, one of the most common groups of children with an intellectual disability. This is particularly true for mathematical learning, an area in which many experience particular difficulty. Objectives: The study set out to evaluate a bespoke digital game in which children learned to select which was "more," a foundational skill for understanding magnitude. Methods: A mixed methods approach was adopted with eight single case studies of children aged 9–14 years. Probes (untaught examples) were introduced to examine progress and the impact on performance in non‐digital contexts. Results: Five pupils improved their performance on the digital games and this was sustained at the time of the delayed post‐test. Four pupils showed improved performance in non‐taught, non‐digital contexts for both taught and untaught ratios. Disaggregated data reveals the variability in performance, with peak performances occurring at different points of the intervention. The introduction of a two‐player version improved performance for five pupils through promoting sustained attention and strategic responses to winning. One child performed at chance level on the digital game throughout but made gains in non‐digital settings. Conclusions: Bespoke learning tools have good potential to promote attention to numerosity. However, progress in digital contexts does not automatically transfer to non‐digital contexts. The study reveals the individual nature of the learning affordances of different pedagogic tools and the place of bespoke games within teachers' repertoires. Lay Description: Research suggests that it is important to tailor intervention to the particular strengths and needs of children with Down syndrome but there are few bespoke games in the field of mathematics.This study focuses on the ability to discriminate between quantities, a foundation for mathematical learning.Children's discrimination of "which is more" improved during the period of intervention and at follow‐up. They did not however automatically transfer these skills to other contexts. Many attended best when playing the game with another person. Additionally, one pupil performed better on non‐digital activities.The study emphasizes the importance of practitioners looking carefully at each pupil's performance in a range of digital and nondigital contexts, to identify which best meets their current learning needs. [ABSTRACT FROM AUTHOR]

Observers can quickly estimate the quantity of sets of visual elements. Many aspects of this ability have been studied and the underlying system has been called the Approximate Number Sense (Dehaene, 2011). Specific visual properties, such as size and clustering of the elements, can bias an estimate. For intermediate numerical quantities at low density (above five, but before texturization), human performance is predicted by a model based on the region of influence of elements (occupancy model: Allïk & Tuulmets, 1991). For random 2D configurations we computed ten indices based on graph theory, and we compared them with the occupancy model: independence number, domination, connected components, local clustering coefficient, global clustering coefficient, random walk, eigenvector centrality, maximum clique, total degree of connectivity, and total edge length. We made comparisons across a range of parameters, and we varied the size of the region of influence around each element. The analysis of the pattern of correlations suggests two main groups of graph-based measures. The first group is sensitive to the presence of local clustering of elements, the second seems more sensitive to density and the way information spreads in graphs. Empirical work on perception of numerosity may benefit from comparing, or controlling for, these properties. [ABSTRACT FROM AUTHOR]

Numerical cognition is ubiquitous in the animal kingdom. Domestic chicks are a widely used developmental model for studying numerical cognition. Soon after hatching, chicks can perform sophisticated numerical tasks. Nevertheless, the neural basis of their numerical abilities has remained unknown. Here, we describe number neurons in the caudal nidopallium (functionally equivalent to the mammalian prefrontal cortex) of young domestic chicks. Number neurons that we found in young chicks showed remarkable similarities to those in the prefrontal cortex and caudal nidopallium of adult animals. Thus, our results suggest that numerosity perception based on number neurons might be an inborn feature of the vertebrate brain. [ABSTRACT FROM AUTHOR]

Copyright of Africa Spectrum is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Previous studies using an affective priming paradigm have shown that valenced chords (e.g., consonant–positive; dissonant–negative) facilitate the evaluation of similarly valenced target words. The role of numerosity (the total number of pitches in a chord) and timbre has not yet been systematically investigated in previous priming studies using consonant/dissonant chords. An experiment was conducted in which 40 participants evaluated positive and negative target words with consonant/dissonant chords used as affective primes. Eight distinct chords (four consonant and four dissonant) were used as primes; the consonant and dissonant chords were equally divided to comprise either two (i.e., interval) or four (i.e., tetrad) pitches. Each chord was played with two distinct timbres (piano and harmonium), resulting in a total of 16 chords. Results showed that congruent chord–word pairings resulted in faster reaction times, and this finding was in line with previous research using consonant/dissonant chords as primes. However, this effect was present only with tetrad chords, suggesting that numerosity influences affective priming done with chords. There were no significant effects of timbre or the musical sophistication of the participants. Arguments are made as to why higher pitch numerosity in chords (resulting in acoustic complexity) might influence the evaluation of valenced target words. [ABSTRACT FROM AUTHOR]

This paper proposes a new natural kinds framework according to which kindhood is relational, dynamic, and scale-relative. Reflecting on the ontogenesis of a scientific classification, I argue that there are two distinct conceptual stages to a scientific classification: a first stage in which enough entities and relations must be authenticated for kindhood to emerge and a second in which the nature of authenticated entities and relations is investigated. The new framework is scale-relative and explains both the changing nature of the entities and relations themselves as well as the changing nature of the classifications in which they are organised. [ABSTRACT FROM AUTHOR]

Previous studies have shown that self-generated stimuli in auditory, visual, and somatosensory domains are attenuated, producing decreased behavioral and neural responses compared with the same stimuli that are externally generated. Yet, whether such attenuation also occurs for higher-level cognitive functions beyond sensorimotor processing remains unknown. In this study, we assessed whether cognitive functions such as numerosity estimations are subject to attenuation in 56 healthy participants (32 women). We designed a task allowing the controlled comparison of numerosity estimations for self-generated (active condition) and externally generated (passive condition) words. Our behavioral results showed a larger underestimation of self-generated compared with externally generated words, suggesting that numerosity estimations for self-generated words are attenuated. Moreover, the linear relationship between the reported and actual number of words was stronger for self-generated words, although the ability to track errors about numerosity estimations was similar across conditions. Neuroimaging results revealed that numerosity underestimation involved increased functional connectivity between the right intraparietal sulcus and an extended network (bilateral supplementary motor area, left inferior parietal lobule, and left superior temporal gyrus) when estimating the number of self-generated versus externally generated words. We interpret our results in light of two models of attenuation and discuss their perceptual versus cognitive origins. [ABSTRACT FROM AUTHOR]

It is debated whether the representation of numbers is endowed with a directional-spatial component so that perceiving small-magnitude numbers triggers leftward shifts of attention and perceiving large-magnitude numbers rightward shifts. Contrary to initial findings, recent investigations have demonstrated that centrally presented small-magnitude and large-magnitude Arabic numbers do not cause leftward and rightward shifts of attention, respectively. Here we verified whether perceiving small or large non-symbolic numerosities (i.e., clouds of dots) drives attention to the left or the right side of space, respectively. In experiment 1, participants were presented with central small (1, 2) vs large-numerosity (8, 9) clouds of dots followed by an imperative target in the left or right side of space. In experiment 2, a central cloud of dots (i.e., five dots) was followed by the simultaneous presentation of two identical dot-clouds, one on the left and one on the right side of space. Lateral clouds were both lower (1, 2) or higher in numerosity (8, 9) than the central cloud. After a variable delay, one of the two lateral clouds turned red and participants had to signal the colour change through a unimanual response. We found that (a) in Experiment 1, the small vs large numerosity of the central cloud of dots did not speed up the detection of left vs right targets, respectively, (b) in Experiment 2, the detection of colour change was not faster in the left side of space when lateral clouds were smaller in numerosity than the central reference and in the right side when clouds were larger in numerosity. These findings show that perceiving non-symbolic numerosity does not cause automatic shifts of spatial attention and suggests no inherent association between the representation of numerosity and that of directional space. [ABSTRACT FROM AUTHOR]

Four perspectives on numerical origins are examined. The nativist model sees numbers as an aspect of numerosity, the biologically endowed ability to appreciate quantity that humans share with other species. The linguistic model sees numbers as a function of language. The embodied model sees numbers as conceptual metaphors informed by physical experience and expressed in language. Finally, the extended model sees numbers as conceptual outcomes of a cognitive system that includes material forms as constitutive components. If numerical origins are to be found, each perspective must address one or more critical questions that will require working across discipline boundaries. [ABSTRACT FROM AUTHOR]

A probability distribution is regular if it does not assign probability zero to any possible event. Williamson (Analysis, 67, 173–180, 2007) argued that we should not require probabilities to be regular, for if we do, certain "isomorphic" physical events (infinite sequences of coin flip outcomes) must have different probabilities, which is implausible. His remarks suggest an assumption that chances are determined by intrinsic, qualitative circumstances. Weintraub (Analysis, 68, 247–250, 2008) responds that Williamson's coin flip events differ in their inclusion relations to each other, or the inclusion relations between their times, and this can account for their differences in probability. Haverkamp and Schulz (Erkenntnis, 76, 395–402, 2012) rebut Weintraub, but their rebuttal fails because the events in their example are even less symmetric than Williamson's. However, Weintraub's argument also fails, for it ignores the distinction between intrinsic, qualitative differences and relations of time and bare identity. Weintraub could rescue her argument by claiming that the events differ in duration, under a non-standard and problematic conception of duration. However, we can modify Williamson's example with Special Relativity so that there is no absolute inclusion relation between the times, and neither event has longer duration except relative to certain reference frames. Hence, Weintraub's responses do not apply unless chance is observer-relative, which is also problematic. Finally, another symmetry argument defeats even the appeal to frame-dependent durations, for there the events have the same finite duration and are entirely disjoint, as are their respective times and places. [ABSTRACT FROM AUTHOR]

Extracting the number of objects in perceived scenes is a fundamental cognitive ability. Number processing is proposed to rely on two consecutive stages: an early object location map that captures individuated objects in a location‐specific way and a subsequent location‐invariant representation that captures numerosity at an abstract level. However, it is unclear whether this framework applies to small numerosities that can be individuated at once ("subitized"). Here, we reanalyzed data from two electroencephalography (EEG) experiments using multivariate pattern decoding to identify location‐specific and location‐invariant stages of numerosity processing in the subitizing range. In these experiments, one to three targets were presented in the left or right hemifield, which allowed for decoding target numerosity within each hemifield separately (location specific) or across hemifields (location invariant). Experiment 1 indicated the presence of a location‐specific stage (180–200 ms after stimulus), followed by a location‐invariant stage (300 ms after stimulus). A time‐by‐channel searchlight analysis revealed that the early location‐specific stage is most evident at occipital channels, whereas the late location‐invariant stage is most evident at parietal channels. Experiment 2 showed that both location‐specific and location‐invariant components are engaged only during tasks that explicitly require numerosity processing, ruling out automatic, and passive recording of numerosity. These results suggest that numerosity coding in subitizing is strongly grounded on an attention‐based, location‐specific stage. This stage overlaps with the subsequent activation of a location‐invariant stage, where a full representation of numerosity is finalized. Taken together, our findings provide clear evidence for a temporal and spatial segregation of location‐specific and location‐invariant numerosity coding of small object numerosities. [ABSTRACT FROM AUTHOR]

Finger-Braille is a tactile communication method used by people who are Deafblind. Individuals communicate Finger-Braille messages with combinations of taps on three fingers of each of the hands of the person receiving the communication. Devices have been developed to produce Finger-Braille symbols using different tactile stimulation methods. Before engaging in communication studies based on technologically-mediated Finger-Braille, we evaluated the relative efficacy of these methods by comparing two devices similarly constructed; the first based on widely employed eccentric rotating-mass vibrating motors and the other using specifically designed tapping actuators. We asked volunteers to identify the numerosity of presented items and for each device we measured (1) error-rate, (2) reaction time, (3) confidence ratings, and (4) a comparison of confidence ratings to actual performance. The four measures obtained for each device showed a net advantage of the tapping stimulation method over the method of vibrations. In this article, we conclude that the tapping stimulation method is recommended for use in the design of tactile communication devices based on Finger-Braille and fingerspelling methods reliant on finger tapping actions. The results did not demonstrate clear evidence for tactile subitising with passively experienced stimulation on the fingers. [ABSTRACT FROM AUTHOR]

Both animal and human studies on numerosity have shown the importance of the parietal cortex for numerosity processing. However, most studies have focused on the perceptual processing of numerosity. Still, it is unclear how and where numerosity information is coded when this information is retained during a working memory delay phase. Such temporal storage could be realized by the same structures as perceptual processes, or be transformed to a more abstract representation, potentially involving prefrontal regions. FMRI decoding studies allow the identification of brain areas that exhibit multi‐voxel activation patterns specific to the content of working memory. Here, we used an assumption‐free searchlight‐decoding approach to test where numerosity‐specific codes can be found during a 12 s retention period. Participants (n = 24) performed a retro‐cue delayed match‐to‐sample task, in which numerosity information was presented as visual dot arrays. We found mnemonic numerosity‐specific activation in the right lateral portion of the intraparietal sulcus; an area well‐known for perceptual processing of numerosity. The applied retro‐cue design dissociated working memory delay activity from perceptual processes and showed that the intraparietal sulcus also maintained working memory representation independent of perception. [ABSTRACT FROM AUTHOR]

Rodents can be trained to associate different durations with different stimuli (e.g., light/sound). When the associated stimuli are presented together, maximal responding is observed around the average of individual durations (akin to averaging). The current study investigated whether mice can also average independently trained numerosities. Mice were initially trained to make 10 or 20 lever presses on a single (run) lever to obtain a reward and each fixed-ratio schedule was signaled either with an auditory or visual stimulus. Then, mice were trained to press another lever to obtain the reward after they responded on the run lever for the minimum number of presses [Fixed Consecutive Number (FCN)-10 or -20 trials] signaled by the corresponding discriminative stimulus. Following this training, FCN trials with the compound stimulus were introduced to test the counting behavior of mice when they encountered conflicting information regarding the number of responses required to obtain the reward. Our results showed that the numbers of responses on these compound test trials were around the average of the number of responses in FCN-10 and FCN-20 trials particularly when the auditory stimulus was associated with a fewer number of required responses. The counting strategy explained the behavior of the majority of the mice in the FCN-Compound test trials (as opposed to the timing strategy). The number of responses in FCN-Compound trials was accounted for equally well by the arithmetic, geometric, and Bayesian averages of the number of responses observed in FCN-10 and FCN-20 trials. [ABSTRACT FROM AUTHOR]

Humans and other animal species are endowed with the ability to sense, represent, and mentally manipulate the number of items in a set without needing to count them. One central hypothesis is that this ability relies on an automated functional system dedicated to numerosity, the perception of the discrete numerical magnitude of a set of items. This system has classically been associated with intraparietal regions, however accumulating evidence in favor of an early visual number sense calls into question the functional role of parietal regions in numerosity processing. Targeting specifically numerosity among other visual features in the earliest stages of processing requires high temporal and spatial resolution. We used frequency-tagged magnetoencephalography to investigate the early automatic processing of numerical magnitudes and measured the steady-state brain responses specifically evoked by numerical and other visual changes in the visual scene. The neuromagnetic responses showed implicit discrimination of numerosity, total occupied area, and convex hull. The source reconstruction corresponding to the implicit discrimination responses showed common and separate sources along the ventral and dorsal visual pathways. Occipital sources attested the perceptual salience of numerosity similarly to both other implicitly discriminable visual features. Crucially, we found parietal responses uniquely associated with numerosity discrimination, showing automatic processing of numerosity in the parietal cortex, even when not relevant to the task. Taken together, these results provide further insights into the functional roles of parietal and occipital regions in numerosity encoding along the visual hierarchy. [ABSTRACT FROM AUTHOR]

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition. [ABSTRACT FROM AUTHOR]

When presented with resources that differ in quantity, many animals use a numerosity system to discriminate between them. One taxonomically widespread system is the approximate number system. This is a numerosity system that allows the rapid evaluation of the number of objects in a group and which is regulated by Weber's Law. Here we investigated whether wild, free-living rufous hummingbirds (Selasphorus rufus) possess an approximate number system. The hummingbirds were presented with two experiments. In the first we investigated whether hummingbirds spontaneously chose an array containing more flowers than an alternate array. In the second we asked whether the hummingbirds could learn to use numerosity as a cue to which of two arrays contained the better reward. The birds did not spontaneously prefer an array containing more flowers. After minimal training, however, they learned to choose the more numerous array and could differentiate between arrays of five and seven flowers. These data support the presence of an approximate number system in the rufous hummingbird. It seems plausible that having such a system would enable much more efficient foraging in this species. [ABSTRACT FROM AUTHOR]

Children's spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children's focus on numerosity, may reveal whether task materials can implicitly prompt children to focus on numerosity. In two studies, we replicate earlier findings showing an effect of task context on children's performance on the AtN: When asked to identify one or more matches to a target picture from an array of four options, the frequency with which preschoolers and adults identify a numerosity-based match varies as a function of the features on which the remaining match options are based. We addressed a limitation of the original AtN study by including novel combinations of features as additional trials, with which we continued to demonstrate contextual effects. We also showed that adults seemed more susceptible than children to be primed to attend to numerosity on subsequent trials. Children's focus on numerosity under these experimental conditions was remarkably low. We discuss the implications of these findings for better understanding the SFON construct. [ABSTRACT FROM AUTHOR]

Individuals have a tendency to fixate on large numbers and ignore other relevant information in their decision making process. The numerosity heuristic, a cognitive bias, is the first behavioral hypothesis to explain why investors prefer to receive more shares (rather than less shares) in a stock split even though the aggregate economic value is the same. For forward splits, after controlling for the positive signaling of improved earnings growth and liquidity from the split announcement, the stock price reacts positively to the larger number of shares issued. More importantly, the use of a dual class numerosity model can explain why most conventional hypotheses fail to explain the negative stock price reaction to reverse splits. Given a typical bearish outlook associated with a reverse stock split, investors' cognitive resources have already been conditioned to derive a systematic conclusion to sell the stock at the higher price. Focusing only on large stock price numerosity, investors are incorrectly inferring a higher investment value. As the high numerosity encourages bearish investors to sell at the higher perceived investment value, the stock returns react more negatively to the higher post-reverse split price level. In both forward and reverse split cases, investors react to high numerosity. [ABSTRACT FROM AUTHOR]

In the last few years, the existence of a pure number sense has been challenged. Recent studies suggest that numerosity processing is influenced not only by the number of elements in a display but also by continuous magnitudes, such as the size of the elements. The aim of our study was to replicate and extend the findings by Gebuis and Reynvoet, who systematically manipulated different continuous magnitudes either congruently or incongruently with discrete numerosity. We were particularly interested in finding the same pattern of congruency effects and assess its stability and robustness as this pattern indicates a complex influence of continuous magnitudes on numerosity judgements. We did so by showing stimuli of different conditions either in separate blocks or mixed together while participants solved a dot comparison task. Our results are in line with the notion that discrete number and continuous magnitudes are integrated in numerosity judgements by means of a weighing process. Moreover, our findings suggest that this integration is modified by the mode of presentation (blocked vs. mixed). [ABSTRACT FROM AUTHOR]

Pre literacy skills in young children have been well established. Explorations of the parallel concept of pre mathematic skills in young children are minimal. Recommendations for how to engage young children, specifically infants, in math have been limited to caregiver counting games. This colloquium presents an example of how an 11-month-old is able to demonstrate pre mathematics skills. This raises the question of beyond caregivers counting, what are early numerosity activities for preverbal infants? [ABSTRACT FROM AUTHOR]

High-level cognitive capacities that serve communication, reasoning, and calculation are essential for finding our way in the world. But whether and to what extent these complex behaviors share the same neuronal substrate are still unresolved questions. The present study separated the aspects of logic from language and numerosity—mental faculties whose distinctness has been debated for centuries—and identified a new cytoarchitectonic area as correlate for an operation involving logical negation. A novel experimental paradigm that was implemented here in an RT/fMRI study showed a single cluster of activity that pertains to logical negation. It was distinct from clusters that were activated by numerical comparison and from the traditional language regions. The localization of this cluster was described by a newly identified cytoarchitectonic area in the left anterior insula, ventro-medial to Broca's region. We provide evidence for the congruence between the histologically and functionally defined regions on multiple measures. Its position in the left anterior insula suggests that it functions as a mediator between language and reasoning areas. [ABSTRACT FROM AUTHOR]

Products can be described by different numbers of attributes, but can the mere number of attributes presented across a choice set influence what type of options people choose? This article demonstrates that attribute numerosity tends to benefit certain types of options more than others and consequently has systematic effects on choice. Because attributes often serve as a heuristic cue for product usefulness, they benefit options that people perceive as relatively inferior on this dimension. Consistent with this perspective, five studies demonstrate that attribute numerosity benefits hedonic more than utilitarian options by increasing the extent to which the former appear useful. Consequently, increasing attribute quantity equally across the choice set shifts choice toward hedonic options, regardless of whether the attributes are hedonic, utilitarian, or mixed in nature. Consistent with this conceptualization, these effects become amplified when decision makers engage in heuristic processing and when priming makes usefulness salient. The findings have important implications for how marketers present attribute information, for public policy and consumer welfare, and for understanding argument numerosity effects in persuasion more broadly. [ABSTRACT FROM AUTHOR]