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This study presents a new theory for how animals and humans estimate numbers, explaining imprecise numerical estimation through information processing limits and sensory noise. The model accurately predicts human numerical perception over time.

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Area of Science:

  • Cognitive Science
  • Comparative Psychology
  • Neuroscience

Background:

  • Non-symbolic numerical quantity estimation is crucial for survival across species.
  • Despite its importance, this sense is imprecise and biased, lacking a clear explanation.

Purpose of the Study:

  • To develop a unified normative theory for numerosity estimation.
  • To explain imprecision and biases in numerical cognition through a single framework.

Main Methods:

  • Developed a normative theory incorporating Brownian diffusion noise, logarithmic encoding, and Bayesian decoding.
  • Modeled information processing constraints and time perception in sensory encoding.
  • Compared the proposed model with thermodynamically-inspired bounded rationality.

Main Results:

  • The model predicts the posterior distribution of numerosity estimates based on biological capacity constraints.
  • Accurately predicts human numerosity estimation as a function of temporal exposure.
  • Demonstrates efficient sampling of numerosity information over time in humans.

Conclusions:

  • The proposed mechanism, integrating noise and efficient encoding, explains numerical cognition patterns in humans and animals.
  • This framework offers a parsimonious explanation for the seemingly irrational aspects of numerical estimation.
  • Highlights the role of time perception in noisy, efficient sensory information processing.