Is auditory intensity discrimination a comparison of entropy changes

Abstract

In JASA (97, 1995), Wong & Norwich presented a Weber-fraction equation derived from McConville, Norwich, & Abel (Int J Biomed Comput 27, 1991). The latter modeled two-alternative forced-choice discrimination between stimuli of identical spectra and identical durations “t” but differing intensities I and I+ΔI. Discrimination depended on ΔH(I,t), the change in the information-theoretic entropy over t and ΔI. ΔH(I,t), assumed constant over intensities, emerged as one of five unknowns in a Weber-fraction equation, (ΔI)/I=f(t0,tW,n,β,ΔH(I,t)). McConville et al. presumed values for n and tW. Using (ΔI)/I≈ΔH(I,t)/(IΔt[∂2H/∂I∂t]) and setting Δt=t, f(t0,tW,n,β,ΔH(I,t)) was approximated as g(n,(β/t),ΔH(I,t)) =ΔH(I,t)/(It[∂2H/∂I∂t]), which was then curvefitted to one listener's Weber fractions. The obtained ΔH(I,t) alone was substituted back into f(t0,tW,n,β,ΔH(I,t)), which was then substantiated by curvefitting to the data to reveal the remaining unknowns, t0 and β. McConville et al. had to curvefit, because they model only a single, unspecified forced-choice trial, making ΔI any intensity change; and none of the unknowns could legitimately be presumed. The curvefitting was flawed: the assumption ΔH(I,t)=constant affirms Fechner's postulate; and ∂2H/∂I∂t<0, giving a negative Weber fraction. McConville et al. fail to explain auditory intensity discrimination as a comparison of entropy changes, casting doubt on Wong & Norwich (1995).