An explanation for inconsistency between psychophysical functions derived from different scaling methods on a prothetic continuum

In this note is proposed an hypothetical explanation for the question of why, on a prothetic continuum, a psychophysical function obtained by direct scaling is inconsistent with that obtained by indirect scaling. We explain by making the assumption that there are two stages of sensory processes which transform a given stimulus value to a perceived value serially by logarithmic and exponential functions. It is illustrated that, on a prothetic continuum, a logarithmic function should be obtained by direct scaling and a power function should be obtained by indirect scaling if our assumption is expanded mathematically.