Brief articleSubitizing reflects visuo-spatial object individuation capacity
Highlights
► Subitizing may reflect a capacity limited mechanism for multiple object individuation. ► We compare capacity in enumeration and in visuo-spatial short term memory tasks. ► Capacity in the two tasks correlate across subjects and is reduced in dual task conditions. ► Results are predicted assuming a common mechanism for individuation.
Introduction
The exact nature and origin of subitizing, the immediate apprehension of the exact number of items in small sets, is currently debated. One hypothesis posits that it reflects a numerosity estimation process common for small and large sets, which precision decreases as the number of items increases, according to Weber’s law (Dehaene and Changeux, 1993, Gallistel and Gelman, 1991). In a previous investigation, however, we have discarded this account by showing that enumeration responses (in terms of accuracy, estimates distributions, and reaction times) dramatically differ for sets of few items compared to sets with a large number of items with identical ratios (e.g. 1, 2, 3, … , 8 vs. 10, 20, 30, … , 80). Moreover, according to the single estimation process hypothesis, individual variability in subitizing capacity should correlate with the individual variability in the precision of large numerosity estimation. Thus, for example, a small subitizing capacity should indicate a rough internal representation of numerical quantity, which, in turns, should produce low accuracy in large numerosity estimation. Contrary to this prediction, however, we have shown that the two capacities do not correlate across subjects (Revkin, Piazza, Izard, Cohen, & Dehaene, 2008).
An alternative view on subitizing proposes that it reflects a mechanism of individuating multiple objects in parallel (Trick & Pylyshyn, 1994) that is not specific to the domain of number processing. The term “individuation” is here used to emphasize the fact that items are, through this mechanism, perceived as specific individuals with a given identity and spatial location. According to this view, such parallel individuation mechanism would be common to any tasks requiring multiple objects individuation. One such task is visual working memory (VWM), where subjects encode multiple objects at a time to subsequently compare them to other objects. Like subitizing, visual working memory also shows capacity limits of around three to four items (Luck & Vogel, 1997), even if the exact estimates of such limit are not fixed, but vary depending on the participants and task parameters (Alvarez and Cavanagh, 2004, Bays and Husain, 2008, Melcher, 2001, Melcher and Morrone, 2007).
In the developmental literature, this multiple object tracking mechanism is sometimes defined as based on “object files”, intended as temporary representations of individual objects from a scene (for a review, see (Feigenson, Dehaene, & Spelke, 2004)). Physiologically, we may think of this mechanism as an internal map whereby a limited number of salient objects, as well as their locations can be highlighted in parallel and subsequently used for actions such as grasping or eye movements (Xu & Chun, 2009), or for cognitive tasks such as matching them with other objects or assessing their number (Gottlieb, 2007).
We thus reason that if subitizing relies on such a domain-general process of visuo-spatial individuation, which is not specific to numerical judgements, then the existing inter-individual variability in subitizing (Revkin et al., 2008) and VWM capacity (Vogel & Machizawa, 2004) should tightly correlate, in the absence of correlation between either of these measures with the precision of large numerosity estimation (Halberda et al., 2008, Piazza et al., 2010). We further reasoned that if the individuation process needs to be accessed simultaneously by the requirements of different tasks, as in a dual task condition, then we should observe decreased capacity. According with this idea, even an apparently basic ability like subitizing should be impaired if its core resource (the individuation “map”) is being used for another task. To test this hypothesis, we measured enumeration accuracy with and without a concurrent VWM task. Finally, complementary to this prediction, we also reasoned that if large numerosity estimation abilities do not heavily rely on the individuation map, then they should not be impaired by a concurrent individuation task. Thus, we measured large numerosity comparison performance with and without a concurrent VWM task.
Section snippets
Single task experiment
Sixteen healthy participants (10 males, mean age = 26.2 years), naïve to the scope of the research, gave written informed consent. The experiment took place in a quiet, dimly lit room. Participants sat in front of the computer monitor at a viewing distance of about 50 cm and with their face fixed on a chinrest. Vocal and manual responses were recorded by a microphone and the E-prime response box respectively. Each participant performed the following three tasks, in randomized order.
Single task experiments
In all three tasks we observed the expected patterns of results. In the dots counting task, mean correct response times (RTs) and errors increased with set size (F(7, 105) = 155.279, p = 0.001, and F(7, 105) = 55.95, p = 0.000, respectively), but only starting from numerosity 3 onwards (see Fig. 1, panel B).
We estimated, for each subject, the subitizing capacity (hereafter S) by fitting the full RTs curve with a sigmoid function of numerosity and taking the inflexion point of that curve (Revkin et al.,
Discussion
In conflict with the idea that small numerosities are processed by a Weberian mechanism for extracting numerical information common for large and small numerosity, we found that individual differences in subitizing capacity do not correlate with individual difference in large number estimation precision. Thus, the two mechanisms seem to be of a different nature. This result is in line with recent work in favor of the notion of a dissociation between large and small numerosity processing in
References (30)
- et al.
Core systems of number
Trends in Cognitive Sciences
(2004) From thought to action: The parietal cortex as a bridge between perception, action, and cognition
Neuron
(2007)- et al.
Trans-saccadic perception
Trends in Cognitive Sciences
(2008) Neurocognitive start-up tools for symbolic number representations
Trends in Cognitive Sciences
(2010)- et al.
Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia
Cognition
(2010) - et al.
Tuning curves for approximate numerosity in the human intraparietal sulcus
Neuron
(2004) - et al.
Can subitizing survive the attentional blink? An ERP study
Neuroscience Letters
(2008) - et al.
Selecting and perceiving multiple visual objects
Trends in Cognitive Sciences
(2009) - et al.
The capacity of visual short-term memory is set both by visual information load and by number of objects
Psychological Science
(2004) - et al.
Dynamic shifts of limited working memory resources in human vision
Science
(2008)
Subitizing but not estimation of numerosity requires attentional resources
Journal of Vision
The magical number 4 in short-term memory: A reconsideration of mental storage capacity
Behavioral and Brain Sciences
Symbols and quantities in parietal cortex: Elements of a mathematical theory of number representation and manipulation
Development of elementary numerical abilities: A neuronal model
Journal of Cognitive Neuroscience
Neural measures of individual differences in selecting and tracking multiple moving objects
Journal of Neuroscience
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