Abstract

Anyone who has climbed a mountain before knows that the perceived distance walked depends on more than just its physical length. This intriguing relationship between physical and experienced magnitudes has fascinated researchers across various disciplines for more than 200 years. Part of the enthusiasm is driven by the fact that, although magnitudes, as well as the sensory organs with which we measure them, differ in so many ways, there are unifying principles in behavior common to all types of magnitudes estimated. In this thesis, the general characteristics of human magnitude estimation are studied in the case of visual path integration. The aim is to clarify the role of a-priori knowledge on the estimate of magnitude and to provide a unifying mathematical framework that explains the behavior. In particular, we investigated human linear and angular displacement estimation in different experimental situations with varying experience-dependent and abstract a-priori knowledge. We find systematic behavioral characteristics that are omnipresent in magnitude estimation studies, like the range effect, the regression effect or scalar variability. These characteristics are explained by a general model that combines a logarithmic scaling of magnitudes according to the Weber-Fechner law with the concept of Bayesian inference. The model incorporates apriori knowledge about the stimulus and updates this knowledge on a trial-by-trial basis. The resulting iterative Bayesian estimation accounts for the aforementioned behavioral characteristics and provides a link between the two most well-known laws in psychophysics: the Weber-Fechner and Stevens’ powerlaw. This work provides substantial evidence that magnitude estimation is not purely driven by sensation but underlies perceptual estimation processes that exploit and incorporate different types of information sources, in particular short-term prior experience. The proposed mathematical framework is likely applicable to magnitude estimation across different modalities and consequently contributes to a unifying account of the behavior.