On Eisler's General Psychophysical Differential Equation and His Fechnerian Integration

Abstract

The general psychophysical differential equation (GPDE) for calculating ‘intrasubjective’ relations, is reviewed and it is argued that: (a) the use of calculus and Weber functions are unnecessary for the determination of such relations: simple algebraic methods are available, (b) Taylor's expansion in the derivation of GPDE is not necessary: a short cut method is suggested and applied instead, (c) GPDE is untenable as an empirical model, for it is based on one definition and one assumption which are both arbitrary and purely mathematical, (d) The sources of error in the validation procedures used by Eisler are pointed out; (e) by means of a validity test and the due treatment of a dozen sets of experimental data, the Fechnerian integration as well as GPDE are invalidated.

On Psychophysics in General and the General Psychophysical Differential Equation in Particular

“…T h e data used here derive from an experiment in which the unpleasantness of electrical stimulation was scaled with magnitude estimation and category rating (Ekman, Frankenhaeuser, Levander & Mellis, 1964). (These data have also been treated by Mashhour, 1964. ) This experiment has attracted my attention for three reasons in particular: (I) the authors claim that 'the relation between the category and the magnitude scale in the present experiment, as well as in several other investigations, will have to be described in terms of a different quantitative principle' after having referred to Fechnerian integration (Eider, 1962~2, b, 1963 c), (2) the category scale in this case exhibits an irregularity for the lowermost points and I was interested to see how the GPDE could cope with this, and (3) as will be shown presently, the Weber function for the category ratings is here-unlike other experiments, clearly parabolic.…”

Dissociations in the timing of stationary and moving stimuli.

“…Perceiving the initial phase of a moving stimulus is subject to several psychophysical distortions. For example, subjective estimates of velocity are larger and subjective estimates of temporal duration are smaller at the beginning of a movement with constant velocity (e.g., Mashhour, 1964; Rachlin, 1966; Runeson, 1974). As a consequence, when participants are presented with this movement they have the impression of a deceleration (i.e., a fast movement at the beginning that then slows down), whereas when they see a movement with a “natural” acceleration at the beginning they judge it as having a constant velocity.…”

“…As a consequence, when participants are presented with this movement they have the impression of a deceleration (i.e., a fast movement at the beginning that then slows down), whereas when they see a movement with a “natural” acceleration at the beginning they judge it as having a constant velocity. Another perceptual distortion, namely the effect that perceived velocity decreases with moving distance (e.g., Algom & Cohen-Raz, 1984, 1987; Mashhour, 1964; Müsseler & Neumann, 1992; Rachlin, 1966), might also be the result of the distortion at the initial phase of a movement. In those studies, constant velocity is used, which is perceived as being fast at the beginning.…”

“…There are also hints that these latency differences can be obtained in behavioral tasks; that is, simple reaction to moving stimuli seems to be faster than to stationary stimuli (Mashhour, 1964; Smeets & Brenner, 1995), and reaction time (RT) to movement onset is a decreasing function of stimulus velocity (Ball & Sekuler, 1980; Mashhour, 1964; Tynan & Sekuler, 1982). Unfortunately, these studies deviate in important aspects from the situation in which the Fröhlich effect is observed: In the study by Mashhour (1964), the RT to the sudden appearance of a stationary stimulus was compared with that to the movement onset of a stimulus already present on the screen (the same was true in the studies conducted by Sekuler and coworkers; Ball & Sekuler, 1980; Tynan & Sekuler, 1982). More critically, Mashhour observed the RT advantage for moving stimuli in only 6 of 10 participants.…”

Magnitude scales, category scales, and the general psychophysical differential equation

“…Since integrating has a certain data smoothing consequence, thereby leading to a decrease in sensitivity, studying Equation 2 directly rather than after integration should give a clearer picture of the correctness of the GPDE (cf. Mashour, 1964).…”