Increasing entropy reduces perceived numerosity throughout the lifespan.

Numerical illusions may provide a powerful window into the mechanisms that give rise to our visual number sense. Recent research has shown that similarly oriented elements appear more numerous than randomly oriented elements in an array. Here we examine whether the orientation coherence illusion is a more general byproduct of the effect of entropy on numerical information-processing. Participants engaged in an ordinal numerical comparison task where the color entropy of arrays was manipulated. We found that arrays with low color entropy were perceived as more numerous than arrays with high color entropy (Experiments 1 and 2), suggesting that the coherence illusion on numerosity perception is not specific to a particular visual property (e.g., orientation) but instead that the entropy of visual arrays more generally affects numerical processing. In Experiment 3, we explored the developmental trajectory of the color entropy effect in children aged 5 to 17 and found that the strength of the coherence illusion increases into adulthood, raising intriguing questions as to how perceptual experiences influence the progression of this numerosity illusion. We consider a recently proposed resource-rational model as a framework for understanding the entropy effect on numerosity perception under an information-theoretic perspective.