Direct evidence for logarithmic magnitude representation in the central nervous system

Fechner's law proposes a logarithmic relationship between the physical intensity and perceived magnitude of a stimulus. The principle of logarithmic magnitude representation has been extensively utilized in various theoretical frameworks. Although the neural correlates of Weber's law have been considered as possible evidence for Fechner's law, there is still a lack of direct evidence for a logarithmic representation in the central nervous system. In our study, participants were asked to reproduce the time intervals between two circles and ignore their spatial distances while electroencephalogram (EEG) signals were recorded synchronously. Behavioral results showed that a Bayesian model, which assumes a logarithmic representation of spatiotemporal information, was better at predicting production times than a model relying on a linear representation. The EEG results revealed that P2 and P3b amplitudes increased linearly with the logarithmic transformation of spatiotemporal information, and these event-related potentials were localized in the parietal cortex. Our study provides direct evidence supporting logarithmic magnitude representation in the central nervous system.