Emmanuel M. Pothos, a cognitive psychologist, has contributed to research exploring the approximate number system (ANS), a cognitive system that supports the estimation of magnitude without relying on language or symbols. His work often employs computational modeling and rational analysis to understand how cognitive systems represent and process information.
Rational analysis, in the context of the ANS, seeks to understand why cognitive systems represent numbers with decreasing fidelity as the numbers get larger. This means investigating why higher numbers are represented with less absolute precision than lower numbers, often formalized as a logarithmic mapping. This approach assumes that there are limited representational resources and that the system seeks to minimize the error between the input and its internal representation, especially for frequently encountered numbers.
In a rational analysis, the aim is to find the “best” mapping between external cardinality (actual number) and internal representation, considering the trade-off between fidelity and limited cognitive resources. This involves minimizing the expected difference between the original input and what a corrupted internal representation signifies, particularly for frequently used numbers.
Pothos’ work, along with others, suggests that the characteristic signatures of the ANS, such as ratio-dependent discrimination, can be understood as an efficient strategy for representing numbers within a bounded psychological space. This rational analysis approach provides a framework for understanding how the ANS has evolved or developed to optimally represent numerical information given the constraints of the cognitive system and the statistical properties of the environment.
- Piantadosi, S. T. (2016). A rational analysis of the approximate number system. Psychonomic Bulletin & Review, 23(3), 877–886. https://doi.org/10.3758/s13423-015-0968-9. Discusses logarithmic mappings, relevant to exponential scales in the model.
- Pothos, E. M., & Busemeyer, J. R. (2022). Quantum Cognition, Annu. Rev. Psychol. 2022. 73:749–78.