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Uncertainty and Prior Assumptions, Rather Than Innate Logarithmic Encoding, Explain Nonlinear Number-to-Space Mapping
Guido Marco Cicchini1, Giovanni Anobile2, Eleonora Chelli2
1Institute of Neuroscience, National Research Council, Pisa, Italy.
Psychological Science
|December 22, 2021
Summary
Human number and color mapping show non-linear patterns. This study suggests these non-linearities arise from contextual Bayesian inference, not inherent logarithmic encoding.
Area of Science:
- Cognitive Psychology
- Neuroscience
- Computational Modeling
Background:
- Number-to-space mapping is often non-veridical, exhibiting compressive nonlinearity.
- This nonlinearity has been attributed to intrinsic logarithmic encoding of numerical values.
Purpose of the Study:
- To investigate the underlying mechanisms of non-veridical number-to-space mapping.
- To test whether contextual Bayesian inference explains observed nonlinearities, challenging the intrinsic logarithmic encoding hypothesis.
Main Methods:
- Adult participants (N=78) mapped dot arrays onto a number line over nine trials.
- A separate group (N=90) performed a color-line task, mapping noise-perturbed colors to a color line.
Main Results:
- Initial number mapping was compressed, becoming more linear with practice.
- Both logarithmic and a parameter-free Bayesian model of central tendency described the data.
- Color mapping exhibited logarithmic or exponential nonlinearity depending on noise distribution, supporting Bayesian inference.
Conclusions:
- Nonlinearity in number and color mapping reflects contextual Bayesian inference.
- This challenges the notion of intrinsic logarithmic encoding for numerical values.
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