December 2022
Volume 22, Issue 14
Open Access
Vision Sciences Society Annual Meeting Abstract  |   December 2022
Number, not uncertainty, drives logarithmic compression of numerosity estimates
Author Affiliations
  • Hyekyung Park
    The Ohio State University
  • John E. Opfer
    The Ohio State University
Journal of Vision December 2022, Vol.22, 3107. doi:
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      Hyekyung Park, John E. Opfer; Number, not uncertainty, drives logarithmic compression of numerosity estimates. Journal of Vision 2022;22(14):3107.

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      © ARVO (1962-2015); The Authors (2016-present)

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When estimating the number of dots on a number line, logarithmicity of estimates typically increases with the range of numbers tested. This effect may reflect a logarithmic encoding of numbers (Dehaene et al, 2008). An alternative hypothesis is that numerosity is encoded linearly, but uncertainty about large numbers drives logarithmic compression (Pomé et al, 2021). We tested these two hypotheses by orthogonally manipulating number and entropy, an information-theoretic measure of uncertainty. In the experiment, 163 participants estimated the numerosity of a group of dots in four conditions. The range of numbers was either 0 to 30 (small number) or 0 to 100 (large number). Entropy was manipulated by using one (low entropy) or multiple (high entropy) dot colors. A multiple regression indicated logarithmicity increased with numerical range (b = .25, p < .01), but was not affected by perceptual entropy (b = .04, p = .66). This result suggests that objective uncertainty (perceptual entropy) does not drive logarithmic compression of estimates. Next, we investigated the effect of subjective uncertainty on estimates by analyzing variability of estimates. When estimates were analyzed trial-to-trial, variability of estimates increased with trial order (b = .72, p < .001), yet logarithmicity decreased with trial order (b = -.67, p < .001), such that they were negatively correlated (b = -.76, p < .001). Together, the study provides further evidence that numbers are encoded logarithmically, and neither objective uncertainty (perceptual entropy) nor subjective uncertainty (variability) drive logarithmic compression of estimates.


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