Exploring the limits of approximate number perception

How do we perceive the number of objects in a visual scene? Are there limits to how finely we can perceive magnitudes like number? In a series of three empirical chapters, I explore the limits of our perceptual abilities and the perceptual basis of approximate number thoughts. First, I investigate laypeople’s intuitive beliefs about perceptual limits. Additionally, I empirically test whether there is evidence for discrimination limits; that is, can people actually tell which is the larger group between 50 and 51 dots? I find that the JND is highly consistent with naïve theories about perception, yet discrimination data indicates that there is no limit to how small of differences we are able to perceive. Next, I propose a novel modeling approach to quantify the contribution of non-task features during magnitude discrimination task. In contrast to previous modeling attempts, I make use of separate parameters for reliance (how much are you “listening” to this feature?) and precision (how precise is your representation of that feature?). Fitting this model to adult discrimination performance on three magnitude comparison tasks, I find that subjects are using distinct representations for different magnitude comparison tasks, and that precision and reliance should be considered separable contributors to number performance. Finally, I dive into the stimuli themselves to test the widely made claim that non- numerical continuous features pattern with number in the real world. Looking at photographs as well as the illustrations of children’s counting books, I find variability in the extent to which continuous features explain significant variability in number. These features perform comparatively better in photographs, but interestingly, I find that both adult and child estimation based on counting book illustrations is superior to their performance in photographs, which indicates that continuous features are not the primary perceptual basis used to extract number from visual scenes