A Warning to the Human-Factors Engineer: False Derivations of Riesz’s Weber Fraction, Piéron’s Law, and Others Within Norwich et al.’s Entropy Theory of Perception

The Entropy Theory of Perception of Professor K.H. Norwich and various collaborators spans 1975 to 2010. Thirty-five years is a surprisingly long publication life for a mathematical model of perception. Its longevity is no doubt related to its unusual ability to provide derivations, from pure theory, of a large cadre of well-established empirical relations of psychophysics, referred to by Norwich et al. as „laws“. Norwich et al.’s work involves computational biology, because they always started their derivations using the same base equation, whose utility was justified through curve-fitting to various kinds of empirical data (see Norwich, 1993). Norwich et al. intended the scope of their theory to be vast, and so the present paper focuses on just one particular set of derivations. Few people offer firstprinciples derivations of natural relations, making such derivations all the more demanding of our attention. At „Fechner Day 96“, the 12th Annual Meeting of the International Society for Psychophysics, W. Wong and K.H. Norwich introduced „Weber fraction and reaction time from the neural entropy“. Therein they showcased what appeared to be two long-overdue breakthroughs: the first-principles derivation of Riesz’s equation for auditory just-noticeable intensity differences (Riesz, 1928), and the first-principles derivation of Piéron’s empirical relation for the minimum time required for a human subject to signal their perception of a newly presented auditory or visual stimulus (Piéron, 1952). The Wong and Norwich breakthroughs were allowed by a „universal model of single-unit sensory receptor action“ presented in a previous paper (Norwich & Wong, 1995). The present paper summarizes the latter work, as an introduction to Norwich et al.’s Entropy Theory, and then proceeds to scrutinize the Wong and Norwich (1996) derivations. In so doing, it reveals that, unfortunately, the algebra of Wong and Norwich (1996) conceals hidden assumptions, unjustified simplifications, and outright mistakes, which had not been brought to public attention. The problems prove to be uncorrectable. This is all the more important because several of the derivations produced in Wong and Norwich (1996) were presented again later, in Wong and Figueiredo (2002). The problems with the Wong and Norwich (1996) and Wong and Figueiredo (2002) derivations are instructional, as they illustrate just how easily