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.
The role of representational cognitive processes (RCPs) in theories of cognition remains a source of disagreement in philosophy of mind and cognitive neuroscience. These debates are stoked by ...arguments that purport to show that RCPs neither receive support from nor support computational theories of cognition, and that dynamicist Embodied, Embedded, Extended (3E) and radical enactivist views of cognition show that RCPs can either be taken out of our heads or dispensed with entirely. We argue that these criticisms fail. We review familiar arguments for thinking that cognitive processes are representational. Next, we consider the challenge that RCPs neither support nor are supported by computational views of cognition, as well as the challenge that neuro-computational RCPs are rendered superfluous by dynamicist views of cognition. We then consider the challenge that intracranial RCPs are rendered superfluous by 3E and radical enactivist views of cognition. We grant that representation is neither necessary nor sufficient for computation. However, we argue that independent reasons support the explanatory utility of neuro-computational RCPs in dynamicist and 3E accounts of cognition and that radical enactivism's claim that all RCPs are extracranial is mistaken about at least one species of cognitive processing, that of subitizing.
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Much previous research has examined various aspects of auditory processing, including the localization of sounds, and the influence of lexical and indexical information on language processing. In the ...present set of experiments we explored the ability of listeners to estimate the number of speakers in a group solely from the information in an auditory signal. The bound on accurately estimating the number of simultaneous speakers is 3. We suggest that subitization-the ability to estimate numerosity of visual and auditory elements without explicitly counting these elements-rather than the capacity of short-term memory, may underlie this limitation. The cognitive constraint on estimating the number of simultaneous speakers may have implications for a wide variety of seemingly unrelated psychological phenomena.
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Everett’s main claim is that language is a “cultural tool”, created by hominids for communication and social cohesion. I examine the meaning of the expression “cultural tool” in terms of the ...influence of language on culture (i.e. the Sapir-Whorf hypothesis) or of the influence of culture on language (Everett’s hypothesis). I show that these hypotheses are not well-supported by evidence and that language and languages, rather than being “cultural tools” as wholes are rather collections of tools used in different language games, some cultural or social, some cognitive. I conclude that the coincidence between language and culture is due to the fact that both originate from human nature.
Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is ...still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1-8) or by tens (10-80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.
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6.
Search, Enumeration, and Aging Watson, Derrick G; Maylor, Elizabeth A; Bruce, Lucy A. M
Psychology and aging,
06/2005, Volume:
20, Issue:
2
Journal Article
Peer reviewed
Response time (RT) and fixation frequency were measured for young and older adults in search and enumeration tasks under high- and low-attentional competition conditions. There was an age-related ...decrement in search rates for single targets both for RT and fixation frequency, but there was no deficit in enumeration rates either with or without distractors even though serial enumeration rates were much slower than single target search rates. Fixation frequency per item in serial enumeration was much greater than in serial visual search for a single target. Enumerating targets with distractors produced an overall increase in RT and fixation frequency that was greater for older adults. The data are contrary to a generalized slowing account, and an alternative is proposed on the basis of the need to make eye movements in enumeration but not in search tasks.
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7.
The Efficiency of Feature-Based Subitization and Counting Watson, Derrick G; Maylor, Elizabeth A; Bruce, Lucy A. M
Journal of experimental psychology. Human perception and performance,
12/2005, Volume:
31, Issue:
6
Journal Article
Peer reviewed
The enumeration of small numbers of objects (∼4) proceeds rapidly, accurately, and with little effort via a process termed
subitization
. Four experiments examined whether it was possible to subitize ...the number of features rather than objects present in a display. Overall, the findings showed that when features are presented randomly and are uncorrelated with object numerosity, efficient enumeration is not possible. This suggests that the visual system does not have parallel access to multiple feature maps and that subitization processes operate exclusively on representations coding the locations of objects. The data are discussed with respect to theories of visual enumeration and search.
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The ability to represent numbers is a key attribute for both humans and animals. Recent developments in the understanding of numerical processing has led to the proposal that humans utilise two ...independent representations of number, one for real numbers and another for integers. We describe a computational model of small number detection to explore the relationship between these
core systems of number. We use a combination of unsupervised and supervised neural networks to simulate the interaction between the real and integer representations. For real values we use a self-organised spatial representation of number. For integer values we use a supervised network motivated by linguistic processing. During training and testing, the networks exhibit behavioural characteristics such as the number size and numerical distance effects. Each representation is combined using the mixture-of-experts architecture that allows us to model the subitization limit (the maximum number of visual stimuli that can be accurately quantified almost immediately) as the competitive allocation of representations for number detection, where the crossover point between deploying the real and integer representations of number is obtained through a process of learning. Our results suggest that the existence of two core systems of number is at least computationally plausible and further suggests that the subitization limit emerges through the interaction of spatial and linguistic numerical processing. This provides computational evidence for one way in which small and large numbers are related in humans.
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Does colour influence subitization? Puts, Marco J.H.; de Weert, Charles M.M.
Acta psychologica,
10/1997, Volume:
97, Issue:
1
Journal Article
Peer reviewed
Open access
A reaction time experiment was performed with patterns that have a close resemblance to the patterns used in the Bourdon-Vos test. These patterns were of three, four and five dots arranged in ...different familiar shapes. Subjects had to determine as fast as possible whether four dots had been presented. In the Bourdon-Vos test the dots are achromatic, while in this experiment, colour was used as a distractor. The reaction time was the same for the one-colour dot patterns as for the two-colour dot patterns. It is hypothesised that the lack of difference was due to overlearnedness of forms in the classic Bourdon-Vos test. A similar test was performed with only one type of forms. Reaction times were different for one- and two-colour dot patterns in the latter experiment.
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A series of visual enumeration tasks were conducted investigating the role of the dorsal visual stream in motion segmentation. Cortical areas representing the lower visual field have greater ...connections with the parietal cortex and should therefore show an advantage for processes driven by the dorsal stream (Previc, 1990). We looked for differences in processing displays in the upper versus lower visual field when targets required segmentation from distractors in an enumeration task. In a baseline condition, random configurations of moving and static items were presented briefly (200 ms) to the upper or lower visual field. Fast and efficient enumeration took place both for moving targets and for static targets presented alone; there was no effect of visual field. In contrast, for moving targets, a lower visual field advantage was found when the inclusion of static distractors demanded segmentation by motion. This disappeared at the smaller display sizes when the targets were presented in canonical patterns. The results are consistent with segmentation of moving targets from static distractors being mediated by dorsal regions of the visual cortex, particularly under conditions of high load (non-canonical patterns). These regions show greater sensitivity to the lower visual field and to magnocellular-based input.
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