Weber-Fechner Law and the Optimality of the Logarithmic Scale
Weber-Fechner Law states that the perceived intensity is proportional to the logarithm of the stimulus. Recent experiments suggest that this law also holds true for perception of numerosity. Therefore, the use of a logarithmic scale for the quantification of the perceived intensity may also depend on how the cognitive apparatus processes information. If Weber-Fechner law is the result of natural selection, then the logarithmic scale should be better, in some sense, than other biologically feasible scales. We consider the minimization of the relative error as the target of natural selection and we provide a formal proof that the logarithmic scale minimizes the maximal relative error.
weber-fechner law logarithmic scale numerosity relative error quantization