A Computational Test of the Information-Theory Based Entropy Theory of Perception: Does It Actually Generate the Stevens and Weber-Fechner Laws of Sensation?

K.H. Norwich et al. used Shannon Information Theory to derive their Entropy Theory of Perception (1975-present). The Entropy Theory produces the Entropy Equation, which relates the strength of sensation (represented by magnitude estimates) to the intensity of the sensory stimulus. At “high” intensities, the relation is approximately logarithmic, which Norwich et al. dubbed “the Weber-Fechner Law”. At “low” intensities, the relation is approximately a power function, dubbed “Stevens’ Law”. Unfortunately, the Entropy Equation has three unknowns, so that what constitutes “high” and “low” can only be established through curve-fitting. Remarkably, the latter was never done. Establishing parameter values is especially important because one of the unknowns is a power exponent (the “Entropy Exponent”, here denoted y) said to be identical in value to “Stevens’ exponent” (here denoted x). The identity y=x was crucial to the numerous published applications of the Entropy Theory to psychophysical and neurophysiological phenomena. Curve-fitting of the Entropy Equation to magnitude estimates would therefore establish the ranges of the “Weber-Fechner” and “Stevens” laws and reveal whether y=x. The present author did the curve-fitting, following the custom in the literature: logarithmic forms of the Entropy Equation and Stevens’ Law were fitted by least-squares regression to logarithm(magnitude-estimate) vs. logarithm(stimulus-strength) taken from 64 published curves of magnitude estimates. The resulting relation of y to x was broadly scattered; 62/64 times, y exceeded x. In theory, the fitted Entropy Equation allows calculation of the information transmitted in perception. Hence the regressions were re-run conditional to an information transmitted of 2.5 bits/stimulus, the mean value in the literature. y≈1.7x under the constrained regression. Altogether, the purported equality of the Entropy Exponent and Stevens’ exponent was not confirmed. Further, neither the “Weber-Fechner Law” nor the “Stevens’ Law” derived from any fitted Entropy Equation described the entire range of the respective magnitude estimation curve, contrary to the formal use of those laws. Norwich’s later quantification of sensation growth by “physical entropy” makes identical mistakes. All of this emphasizes that the Entropy Theory does not derive rules of sensory perception from information theory, and it is recommended that further attempts to do so should be discouraged. Manuscript received March 25, 2009. Work supported by the author. L. Nizami is presently an Independent Research Scholar in Decatur, GA (404-299-5530; e-mail: [email protected]). Research commenced at Dept. of Psychology, University of Toronto in Mississauga, 3359 Mississauga Rd. N., Mississauga, ON, Canada, and continued at Center for Hearing Research, Boys Town National Research Hospital, Omaha, NE 68131, USA.