On the mathematical form of psychophysical relationships, with special focus on the perception of mechanical properties of solid objects.

Abstract

Because the sensory response to mechanical and other stimuli cannot increase indefinitely, the power law of sensory perception can be valid only within a limited range of stimulus magnitudes. An alternative two-parameter mathematical expression that can describe, at least in principle, psychophysical relationships at any stimulus range is presented. It is shown mathematically, and demonstrated through computer simulation, that unless the stimulus magnitude is too close to the threshold or saturation level, the resulting relationship in logarithmic coordinates is practically identical to that predicted by the power law model. It is also demonstrated that the absolute magnitude of the alternative model’s constants can be very similar to those found for the power law model.