numerical magnitudes
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2021 ◽  
Author(s):  
Julia Bahnmueller ◽  
Roberta Barrocas ◽  
Korbinian Moeller ◽  
Stephanie Roesch

Through repeated use of fingers for counting and representing numerical magnitudes in early childhood, specific finger patterns become associated with mental representations of specific quantities. Although children as young as three years of age already use their fingers for representing numerical quantities, evidence on advantageous recognition of such canonical compared to non-canonical finger patterns as well as its association with numerical skills in young children is scarce. In this study, we investigated the performance of N=101 children aged around four years in canonical vs. non-canonical finger pattern recognition and its concurrent association with skills tapping into children’s’ knowledge about quantity-number linkage. Extending previous findings observed for older children, the present results indicated that despite considerable variability on the individual level performance in canonical finger pattern recognition was better compared to non-canonical finger pattern recognition on the group level. Moreover, both canonical and non-canonical finger pattern recognition was positively correlated with tasks tapping into quantity-number linkage. However, when controlling for verbal counting skills, correlations that remained significant were only found for canonical but not non-canonical finger pattern recognition performance. Overall, these results provide insights into the early onset and significance of the effect of canonicity in finger pattern recognition during early numerical development.


2021 ◽  
Vol 21 (12) ◽  
pp. 6183-6187
Author(s):  
P. K. Das ◽  
J. Pal ◽  
M. Debbarma ◽  
K. P. Ghatak

In this paper we study the Electron Statistics in Heavily Doped N Type-Intrinsic-P Type-Intrinsic structures of non-linear optical, tetragonal and opto-electronic materials in the presence of magnetic quantization. It is found taking such heavily doped structures of Cd3As2, CdGeAs2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y as examples that the Fermi energy (EF) oscillates with inverse quantizing magnetic field (1/B) and increases with increasing electron concentration with different numerical magnitudes which is the signature of respective band structure. The numerical value of the Fermi energy is different in different cases due to the different values of the energy band constants.


2021 ◽  
Author(s):  
H Moriah Sokolowski ◽  
Zachary Hawes ◽  
Tali Leibovich-Raveh ◽  
Daniel Ansari

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (NStudy1 = 80, NStudy2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.


Author(s):  
Mathieu Guillaume ◽  
Charlotte Hendryckx ◽  
Anthony Beuel ◽  
Amandine Van Rinsveld ◽  
Alain Content

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tali Leibovich-Raveh ◽  
Ashael Raveh ◽  
Dana Vilker ◽  
Shai Gabay

AbstractWe make magnitude-related decisions every day, for example, to choose the shortest queue at the grocery store. When making such decisions, which magnitudes do we consider? The dominant theory suggests that our focus is on numerical quantity, i.e., the number of items in a set. This theory leads to quantity-focused research suggesting that discriminating quantities is automatic, innate, and is the basis for mathematical abilities in humans. Another theory suggests, instead, that non-numerical magnitudes, such as the total area of the compared items, are usually what humans rely on, and numerical quantity is used only when required. Since wild animals must make quick magnitude-related decisions to eat, seek shelter, survive, and procreate, studying which magnitudes animals spontaneously use in magnitude-related decisions is a good way to study the relative primacy of numerical quantity versus non-numerical magnitudes. We asked whether, in an animal model, the influence of non-numerical magnitudes on performance in a spontaneous magnitude comparison task is modulated by the number of non-numerical magnitudes that positively correlate with numerical quantity. Our animal model was the Archerfish, a fish that, in the wild, hunts insects by shooting a jet of water at them. These fish were trained to shoot water at artificial targets presented on a computer screen above the water tank. We tested the Archerfish's performance in spontaneous, untrained two-choice magnitude decisions. We found that the fish tended to select the group containing larger non-numerical magnitudes and smaller quantities of dots. The fish selected the group containing more dots mostly when the quantity of the dots was positively correlated with all five different non-numerical magnitudes. The current study adds to the body of studies providing direct evidence that in some cases animals’ magnitude-related decisions are more affected by non-numerical magnitudes than by numerical quantity, putting doubt on the claims that numerical quantity perception is the most basic building block of mathematical abilities.


2021 ◽  
Author(s):  
Lauren S Aulet ◽  
Stella F. Lourenco

Accumulating evidence suggests that there is a spontaneous preference for numerical, compared to non-numerical (e.g., cumulative surface area), information. However, given a paucity of research on the perception of non-numerical magnitudes, it is unclear whether this preference reflects a specific bias towards numerosity, or a general bias towards the most perceptually discriminable dimension. Here, we found that when the number and area of visual dot displays were matched in mathematical ratio, number was more perceptually discriminable than area in both adults and children. Moreover, both adults and children preferentially categorized these ratio-matched stimuli based on number, consistent with previous work. However, when number and area were matched in perceptual discriminability, a different pattern of results emerged. In particular, children preferentially categorized stimuli based on area, suggesting that children’s previously observed number bias was due to a mismatch in the perceptual discriminability of number and area, not an intrinsic salience of number. Interestingly, adults continued to categorize the displays on the basis of number. Altogether, these findings suggest a dominant role of area during childhood, refuting the claim that number is inherently and uniquely salient. Yet they also reveal an increased salience of number that emerges over development. Potential explanations for this developmental shift are discussed.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anuj Shukla ◽  
Raju S. Bapi

AbstractThe processing of time and numbers has been fundamental to human cognition. One of the prominent theories of magnitude processing, a theory of magnitude (ATOM), suggests that a generalized magnitude system processes space, time, and numbers; thereby, the magnitude dimensions could potentially interact with one another. However, more recent studies have found support for domain-specific magnitude processing and argued that the magnitudes related to time and number are processed through distinct mechanisms. Such mixed findings have raised questions about whether these magnitudes are processed independently or share a common processing mechanism. In the present study, we examine the influence of numerical magnitude on temporal processing. To investigate, we conducted two experiments using a temporal comparison task, wherein we presented positive and negative numerical magnitudes (large and small) in a blocked (Experiment-1) and intermixed manner (Experiment-2). Results from experiment-1 suggest that numerical magnitude affects temporal processing only in positive numbers but not for negative numbers. Further, results from experiment-2 indicate that the polarity (positive and negative) of the numbers influences temporal processing instead of the numerical magnitude itself. Overall, the current study seems to suggest that cross-domain interaction of magnitudes arises from attentional mechanisms and may not need to posit a common magnitude processing system.


Author(s):  
Amandine Van Rinsveld ◽  
Vincent Wens ◽  
Mathieu Guillaume ◽  
Anthony Beuel ◽  
Wim Gevers ◽  
...  

Abstract 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 (MEG) 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.


2021 ◽  
Vol 14 ◽  
Author(s):  
Anuj Shukla ◽  
Raju S. Bapi

A Theory of Magnitude (ATOM) suggests that space, time, and quantities are processed through a generalized magnitude system. ATOM posits that task-irrelevant magnitudes interfere with the processing of task-relevant magnitudes as all the magnitudes are processed by a common system. Many behavioral and neuroimaging studies have found support in favor of a common magnitude processing system. However, it is largely unknown whether such cross-domain monotonic mapping arises from a change in the accuracy of the magnitude judgments or results from changes in precision of the processing of magnitude. Therefore, in the present study, we examined whether large numerical magnitude affects temporal accuracy or temporal precision, or both. In other words, whether numerical magnitudes change our temporal experience or simply bias duration judgments. The temporal discrimination (between comparison and standard duration) paradigm was used to present numerical magnitudes (“1,” “5,” and “9”) across varied durations. We estimated temporal accuracy (PSE) and precision (Weber ratio) for each numerical magnitude. The results revealed that temporal accuracy (PSE) for large (9) numerical magnitude was significantly lower than that of small (1) and identical (5) magnitudes. This implies that the temporal duration was overestimated for large (9) numerical magnitude compared to small (1) and identical (5) numerical magnitude, in line with ATOM’s prediction. However, no influence of numerical magnitude was observed on temporal precision (Weber ratio). The findings of the present study suggest that task-irrelevant numerical magnitude selectively affects the accuracy of processing of duration but not duration discrimination itself. Further, we argue that numerical magnitude may not directly affect temporal processing but could influence via attentional mechanisms.


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