OS_28. Numerical cognition
Saturday, October 01st, 2011 [16:20 - 17:20]
OS_28.1 - Emergence of a “visual number sense” in hierarchical generative models
Zorzi, M. 1, 2 & Stoianov, I. 1
1 Dipartimento di Psicologia Generale, University of Padova
2 Center for Cognitive Science, University of Padova
Many animal species have evolved a capacity to estimate the numerosity of visual objects. Though foundational to mathematical learning in humans, the nature of the computations underlying this “visual sense of number” remains controversial. Here we show that visual numerosity emerges as a statistical property of images in “deep networks” that learn a hierarchical generative model of the sensory input. Emergent numerosity detectors in the network’s deepest layer had response profiles resembling that of monkey parietal neurons and their activity supported a numerosity estimation task with the same behavioral signature and performance level shown by humans and animals. The unsuspected simplicity of the underlying neural mechanism fits well with the long phylogenetic history of numerosity perception.
OS_28.2 - Object graspability affects number processing
Ranzini, M. 1 , Anelli, F. 1 , Borghi, A. M. 1, 2 , Carbone, R. 1 , Lugli, L. 1 & Nicoletti, R. 1
1 University of Bologna, Bologna, Italy
2 Institute of Cognitive Science and Technology - CNR, Roma, Italy
Several studies have described common processing between numerical and physical magnitudes, and between number and action. However, they did not control for object graspability (affordance). This study investigates the relationship between numerical magnitude, object size, and affordances in two experiments, without (Experiment 1) or with (Experiment 2) motor involvement (i.e. participants had to hold/grasp an object during the task). The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Numerical magnitude (small vs. large), object size (small vs. large), object type (graspable vs. ungraspable), and order (object-number vs. number-object) were manipulated for each experiment. Experiment 1 showed a facilitation for graspable over ungraspable objects preceded by the numbers presentation, and a numerical magnitude effect after graspable objects presentation. Thus, graspability was more relevant than size for number processing. Experiment 2 demonstrated that motor involvement interfered with graspability, however enhancing the sensibility to both numerical and object size. Overall, these findings demonstrate that not only object size, but also object affordances, which involve the motor system, affect number processing. Crucially, they suggest that abstract and concrete concepts are linked through perception-action systems.
OS_28.3 - Retrieval-induced forgetting in cognitive arithmetic
Campbell, J. , Dowd, R. & Thompson, V.
University of Saskatchewan
We investigated retrieval-induced forgetting (RIF) of simple-addition facts (2 + 3 = 5) from practice of their multiplication counterparts (2 × 3 = 6). Experiment 1 demonstrated a response time cost (RIF) for addition with multiplication practiced in word format (three × four) and addition tested later in digit format (3 + 4). This is evidence that digit and written-word formats for arithmetic accessed a common semantic retrieval network. In Experiment 2, Chinese-English bilinguals presented RIF when multiplication practice and addition test were in the same language relative to different languages. Language-specific RIF implies language-specific memory stores for arithmetic.