Subitizing, unlike estimation, does not process sets in parallel

Subitizing endures in sequential rather than simultaneous comparison tasks

Subitizing is the ability to appraise a number of small quantities (up to four) rapidly and precisely. This system, however, can be impaired by distractors presented along with targets to be enumerated. To better understand whether this limitation arises in perceptual circuits or in the response selection stage, we investigated whether subitizing can endure in simultaneous comparison tasks. Participants were asked to compare the number of dots in two sets on the left and right sides of the screen, presented either simultaneously or sequentially. For comparing within the numerosity range (6-32 dots), both the error rate and reaction time increased steadily as the ratio between the two numbers compared approached "1." Namely, a phenomenon labeled the ratio effect was revealed. For comparison with small numbers (<5), the sequential comparison task was errorless despite the ratio, suggesting the feature of subitizing. Individual efficiency (measured by the inverse efficiency score [IES]) did not correlate between number ranges in sequential comparison, suggesting that distinct mechanisms were involved. However, we found that in simultaneous tasks, error rate and efficiency showed an increase as the ratios of the two numbers compared approached "1." This is similar to the ratio effect revealed in the comparison for moderate numbers. Individual efficiency within these two ranges correlated, indicating that the enumeration within these two ranges was based on a single mechanism. These results suggest that subitizing cannot process sets in parallel, and numerosity takes the job whenever subitizing fails.

Nonatopic Eosinophilic Duodenitis in an Adult: A Case Report and Overview

Eosinophilic duodenitis is an inflammation of the duodenum, characterized by an abundance of eosinophils, typically triggered by hypersensitivity reactions. Typically, recurrent abdominal pain with eosinophilic duodenitis is rare in individuals without a history of atopic conditions like asthma. Here, we present the case of a 62-year-old man who experienced recurrent upper abdominal pain for 12 months and unintended weight loss for the past six months. The patient reported no allergies to food, drugs, or the environment, and has no history of other atopic conditions. Esophagogastroduodenoscopy (EGD) with biopsy of the duodenum and stomach revealed 32 eosinophils per high-power field (HPF), which is mild. Skin prick testing yielded negative results. Following initial treatment with H2 inhibitors, proton pump inhibitors, and budesonide for a total of 12 weeks, the patient reported an improvement in symptoms and subsequent weight gain. This report emphasizes a rare case of eosinophilic duodenitis in a nonatopic individual with a successful treatment regimen. His quality of life improved with weight gain, resolved abdominal pain, and improved appetite. Although the patient's condition lasted about 12 months, our report showcased the importance of timely clinical diagnosis and appropriate combination therapy to alleviate progressive pain associated with eosinophilic duodenitis.

Decision-making from temporally accumulated conflicting evidence: The more the merrier

How do humans evaluate temporally accumulated discrete pieces of evidence and arrive at a decision despite the presence of conflicting evidence? In the present study, we showed human participants a sequential presentation of objects drawn from two novel object categories and asked them to decide whether a given presentation contained more objects from one or the other category. We found that both a more disparate ratio and greater numerosity of objects improved both reaction time (RT) and accuracy. The effect of numerosity was separate from ratio, where with a fixed object ratio, sequences with more total objects had lower RT and lower error rates than those with fewer total objects. We replicated these results across three experiments. Additionally, even with the total presentation duration equated and with the motor response assignment varied from trial to trial, an effect of numerosity was still found in RT. The same RT benefit was also present when objects were shown simultaneously, rather than sequentially. Together, these results showed that, for comparative numerosity judgment involving sequential displays, there was a benefit of numerosity, such that showing more objects independent of the object ratio and the total presentation time led to faster decision performance.

Number comparison under the Ebbinghaus illusion

A series of studies show interest in how visual attributes affect the estimate of object numbers in a scene. In comparison tasks, it is suggested that larger patches are perceived as more numerous. However, the inequality of density, which changes inversely with the area when numerosity remains constant, may mediate the influence of area on numerosity perception. This study aims to explore the role of area and density in the judgment of numerosity. The Ebbinghaus illusion paradigm was adopted to induce differences in the perceived, rather than the physical, area of the two patches to be compared. Participants were asked to compare the area, density, and the number of the two patches in three tasks. To this end, no PSE (point of subjective equality) bias was found in number comparison with randomly distributed dots, although a significant difference was revealed in the perceived area of the two patches. No PSE bias was found in the density comparison, either. For a comparison, density and number tasks were also conducted with regularly distributed dots. No PSE bias was found in density comparison. By contrast, significant PSE bias showed up in number comparison, and larger patches appeared to be more numerous than smaller patches. The density mechanism was proposed as the basis for number comparison with regular patterns. The individual Weber fractions for regular patterns were not correlated with those for random patterns in the number task, but they were correlated with those for both patterns in the density task. To summarize, numerosity is directly sensed, and numerosity perception is not affected by area inequality induced by the Ebbinghaus illusion. In contrast, density and area are combined to infer numerosity when the approximate numerosity mechanism is disrupted by dot distribution.

Iconic Mathematics: Math Designed to Suit the Mind

Mathematics is a struggle for many. To make it more accessible, behavioral and educational scientists are redesigning how it is taught. To a similar end, a few rogue mathematicians and computer scientists are doing something more radical: they are redesigning mathematics itself, improving its ergonomic features. Charles Peirce, an important contributor to ordinary symbolic logic, also introduced a rigorous but non-symbolic, graphical alternative to it that is easier to picture. In the spirit of this iconic logic, George Spencer-Brown founded iconic mathematics. Performing iconic arithmetic, algebra, and even trigonometry, resembles doing calculations on an abacus, which is still popular in education today, has aided humanity for millennia, helps even when it is merely imagined, and ameliorates severe disability in basic computation. Interestingly, whereas some intellectually disabled individuals excel in very complex numerical tasks, others of normal intelligence fail even in very simple ones. A comparison of their wider psychological profiles suggests that iconic mathematics ought to suit the very people traditional mathematics leaves behind.

Numerosity perception is tuned to salient environmental features

Numerosity perception is a key ability to guide behavior. However, current models propose that number units encode an abstract representation of numerosity regardless of the non-numerical attributes of the stimuli, suggesting rather coarse environmental tuning. Here we investigated whether numerosity systems spontaneously adapt to all visible items, or to subsets segregated by salient attributes such as color or pitch. We measured perceived numerosity after participants adapted to highly numerous stimuli with color either matched to or different from the test. Matched colors caused a 25% underestimation of numerosity, while different colors had virtually no effect. This was true both for physically different colors, and for the same colors perceived as different, via a color-assimilation illusion. A similar result occurred in the acoustic domain, where adaptation magnitude was halved when the adaptor and test differed in pitch. Taken together, our results support the idea that numerosity perception is selectively tuned to salient environmental attributes.

Distinct Mechanisms in Number Comparison of Random and Regular Dots: An ERP Study

Numerosity comparison for regular patterns shows different features compared with that for random ones in previous studies, suggesting an underlying mechanism distinct from numerosity. In this study, we went further to compare the event-related potentials (ERP) components in numerosity processing of random and regular patterns, which are identical in all aspects of texture features except for the distribution. ERP components were recorded and analyzed while participants compared which of the two successively presented sets was more numerous. P2p amplitude was revealed to be significantly weaker for regular patterns compared with that for random patterns over right occipital-parietal cites, whereas no difference was found for P1 or N1 components. The difference in P2p amplitude, which is consistent with the behavior dissociation revealed in our previous studies, suggests that regular distribution can trigger distinct processing in numeral comparison tasks. Processing of continuous magnitudes or configuration cannot explain the decrease in P2p amplitude for regular distributed patterns. Therefore, this study further supports that P2p is mediated by numerosity processing.

Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays

‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than can unstructured arrays. Previous research suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays quickly and accurately. Here, we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants can use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150 ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

Effect of Non-canonical Spatial Symmetry on Subitizing

Subitizing refers to ability of people to accurately and effortlessly enumerate a small number of items, with a capacity around four elements. Previous research showed that "canonical" organizations, such as familiar layouts on a dice, can readily improve subitizing performance of people. However, almost all canonical shapes found in the world are also highly symmetrical; therefore, it is unclear whether previously reported facilitative effect of canonical organization is really due to canonicality, or simply driven by spatial symmetry. Here, we investigated the possible effect of symmetry on subitizing by using symmetrical, yet non-canonical, shape structures. These symmetrical layouts were compared with highly controlled random patterns (Experiment 1), as well as fully random and canonical patterns (Experiment 2). Our results showed that symmetry facilitates subitizing performance, but only at set size of 6, suggesting that the effect is insufficient to improve performance of people in the lower or upper range. This was also true, although weaker, in reaction time (RT), error distance measures, and Weber Fractions. On the other hand, canonical layouts produced faster and more accurate subitizing performances across multiple set sizes. We conclude that, although previous findings mixed symmetry in their canonical shapes, their findings on shape canonicality cannot be explained by symmetry alone. We also propose that our symmetrical and canonical results are best explained by the "groupitizing" and pattern recognition accounts, respectively.