Theses Doctoral

The Neurobehavioral Basis of the Parallel Individuation (PI) and Approximation Number System (ANS)

Tang, Jean Ee

Research on numerical cognition proposes that there are two systems for the perception of numerical quantity, a small-number system (1~3) invoking parallel individuation, or “subitizing”, and a large-number system (4+) that is based on Weberian magnitude estimation (Hyde, 2011). Many numerical cognitive neuroscientists have focused on studying how the magnitude of numerosities (small vs. large numbers) and numerical distance (close vs. far differences between numbers) are influential factors when processing numbers and change detection. However, is there a difference when numerosities are increasing or decreasing? The effects of direction on numerical change processing are lesser known.

This 128-channel EEG study investigated the neurobehavioral basis of differentiation between small vs. large-number perception and effects of change directionality. During EEG data collection, participants were sequentially presented with stimulus arrays of 1 to 6 dots, with parameters like size and location controlled for, to minimize varying non-numerical visual cues during habituation. Participants were instructed to press a key whenever they detect a change in the number of dots presented.

The current study adapts a dot-stimuli numerical change study design from Hyde and Spelke (2009, 2012). In their EEG study, the researchers examined event-related-potential (ERP) differences during the processing of small (1, 2, 3) and large (8, 16, 24) numbers. For this study, we chose to examine a narrower numerical range from 1~6, so that small (1, 2, 3) vs. large (4, 5, 6) contrasts were along a numerical continuum. In contrast to Hyde and Spelke (2009, 2012), where participants passively-viewed the sequential presentation of dot arrays, this study employed an active change detection paradigm, where participants’ reaction time (RT) and accuracy in detecting change in the number of dots were recorded.

We investigated the effects of Direction and Size in numerical change detection, where Direction is operationally defined as Decreasing and Increasing change in numeric set size, while Size is divided into Small-to-Small, Large-to-Large and Crossovers. Numerical change conditions were categorized into six groups: “Increasing Small-to-Small” (e.g., 1-to-2, 2-to-3), “Decreasing Small-to-Small” (e.g., 2-to-1, 3-to-2), “Increasing Large-Large” (e.g., 4-to-6, 5-to-6), “Decreasing Large-Large” (e.g., 5-to-4, 6-to-5), Increasing Small-to-Large” (e.g., 2-to-4, 3-to-5, 3-to-6) and “Decreasing Large-to-Small” (e.g., 4-to-2, 5-to-2, 6-to-3), where the last two groups are operationally defined as Crossovers. There was also a “No Change” condition, where the number of dots remain the same for up to five presentations. ERP analyses were conducted for the N1 component (125-200 ms) over the left and right occipital-temporal-parietal (POT) junction and for the P3b component (435-535 ms) over the midline parietal area (Pz).

During the No Change condition, results show that the N1 amplitude was modulated by the cardinal values of the habituated numbers 1~6. Within this continuous range, we found N1 amplitudes commensurate with cardinal values in the small range (1, 2, 3), but not in the large range (4, 5, 6), suggesting that numbers in the subitizing range are individuated as objects in working memory.

Meanwhile, in the Change condition, there was a significant main effect of Direction on N1 peak latency, where the Increasing condition showed earlier peaks. In the Decreasing Small-to-Small condition, N1 amplitudes were the lowest (even lower than N1 peaks for No Change conditions), while the other five Change conditions all produced higher N1 negativities than No Change conditions. These results imply that when the number of dots get small enough to parallel individuate, instead of encoding items into visual short-term memory, the brain is “off-loading” items from our perceptual load.
Intriguingly, although the Decreasing Small-to-Small condition had the lowest N1 negativities, it produced the highest P3b positivity. Distinctions in P3b waveforms reflect a clear categorical break between small vs. large numbers, where easier/small number change conditions have higher amplitudes than harder, large number conditions, suggesting more difficulty with updating the context in the latter. However, in contrast to the earlier N1, there was no main effect of Direction on P3b peak latency, but there was an interaction effect of Direction by Size.

Interestingly, there was also a similar interaction effect of Direction by Size for reaction times, with similar trends showing that Decreasing conditions produced shorter reaction times for the Large-to-Large and Crossover conditions, yet this pattern was reversed in the Small-to-Small condition. This lends more support to the implication of the “off-loading” phenomenon when processing decreases of numerosities in the small range (1~3). Meanwhile, when it comes to context-updating at later stages, and a behavioral response is required for this change detection task, the Large-to-Large condition prove to be the most difficult, as there was lower accuracy, longer reaction times, later and lower P3b peaks.

N1 and P3b amplitudes are complementary to each other, with the early N1 being more sensitive to Direction, and the later P3b being more sensitive to Size. This suggests that the posterior parietal cortex might encode Direction first, followed by Size. This study proposes a model that is an adaptation to the P3b context-updating model (Donchin, 1981), where the early, sensory N1 interplays with the later, cognitive P3b. These findings suggest a neurobehavioral basis for the differentiation of small vs. large number perception at early stages of processing that is sensitive to encoding vs. off-loading objects from perceptual load and visual short-term memory, as well as a later stage that involve higher-order cognitive processing on the magnitude of set size that is employed in numerical change detection tasks.


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More About This Work

Academic Units
Cognitive Studies in Education
Thesis Advisors
Gordon, Peter
Ph.D., Columbia University
Published Here
May 24, 2023