Title: Computational characterization of numerosity perception and encoding
Description: Three sets of numerosity comparison and estimation studies with adult human participants explored mechanisms of numerosity perception and the symbolic encoding of the resultant analog numerical magnitude representations. First, experiments with visual perception of dot-array numerosity and auditory perception of tone-sequence numerosity provided strong support for the hypothesis that numerosity is derived from correlated continuous magnitudes, counter to the prevailing view that numerosity perception depends on a nonverbal counting mechanism such as a functionally specialized accumulator. For a nonverbal counting mechanism, perceived numerosity should be invariant with respect to extrinsic stimulus characteristics like element size and array area. Instead, a first set of experiments showed that perceived numerosity varies parametrically with both of these dimensions, and, moreover, that these effects cannot be attributed to downstream stages of processing. These results are explained by a model in which numerosity is computed, heuristically, as the product of perceived area and element density, two dimensions with slightly different psychophysical exponents. A second set of experiments, with auditory tone sequences, showed that comparison accuracy and numerosity estimates are negatively and positively correlated, respectively, with sequence randomness. This parametric variation is explained by a model in which sequence numerosity is computed from perceived total duration and perceived average interval, where the latter is computed as a geometric rather than arithmetic mean.

Finally, constraints on the interface between symbolic and non-symbolic number representations were investigated in a pair of calibrated-estimation experiments in which participants gave estimated dot-array numerosity before and after a two-point calibration procedure. Three groups were given midrange calibration information implying mapping functions with different slopes. A final group was calibrated veridically, but at the endpoints of the stimulus range. Post-calibration estimates revealed a significant effect of implied slope, but within a constrained range; however, the effect of calibration range was much larger, suggesting that the symbolic/non-symbolic interface cannot be fully characterized by a one- or two-free-parameter mapping function.