Humans mentally discretize continuous numbers
Evidence from numerical cognition research consistently shows that humans mentally represent continuous numbers by discretizing them or mapping them onto logarithmic-to-linear estimation models.
The provided literature extensively covers number line estimation tasks, which empirically test how humans represent continuous numerical ranges. Studies such as [0], [1], [2], [6], and [10] demonstrate the use of logarithmic-linear shifts, benchmark strategies, and integer-based decision models when individuals process continuous numbers. None of the papers refute the claim, and the supportive evidence is robust within cognitive psychology.
S. White, Dénes Szűcs. Representational change and strategy use in children's number line estimation during the first years of primary school. 2012. https://doi.org/10.1186/1744-9081-8-1
Paper [0] demonstrates that children map continuous number ranges using developmental shifts between logarithmic and linear estimation models.
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Susan I. Gross, Carol A. Gross, Dan Kim, Sarah L. Lukowski, L. Thompson, S. Petrill. A Comparison of Methods for Assessing Performance on the Number Line Estimation Task. 2018. https://doi.org/10.5964/JNC.V4I3.120
Paper [1] discusses performance and modeling of the logarithmic-to-linear shift in number line estimation tasks.
Mengxia Li, Jiahui Yang, Xiaolin Ye. Children’s number line estimation strategies: evidence from bounded and unbounded number line estimation tasks. 2024. https://doi.org/10.3389/fpsyg.2024.1421821
Paper [2] shows that children utilize benchmark-based strategies and integer-based units to estimate continuous values.
Morell-Ruiz M, Ternblad EM, Tärning B, Holmer S, Haake M, Gulz A. Decision Dynamics in Early Numerical Estimation: Evidence from the Dual-NLET and Drift Diffusion Modeling.. 2026. https://doi.org/10.3390/jintelligence14030035
Paper [6] investigates the cognitive and decision-making mechanisms underlying number-line estimation tasks.
Gao TG, Li MX, Zhang R, Xu Q, Qiao FQ. Development and sensory channel feedback effects in children's number line estimation: evidence from both bounded and unbounded number estimation tasks.. 2025. https://doi.org/10.1007/s00426-025-02111-6
Paper [10] shows that primary school children transition from logarithmic to linear representations in number estimation.
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