Nonlinear Psychophysical Dynamics

Nonlinear Psychophysical Dynamics

Nonlinear Psychophysical Dynamics

Nonlinear Psychophysical Dynamics


Nonlinear Psychophysical Dynamics utilizes new results in systems theory as a foundation for representing sensory channels as a form of recursive loop processes. It demonstrates that a range of phenomena, previously treated as diverse or anomalous, are more readily seen as related and as the natural consequence of self-regulation and nonlinearity. Some cases with appropriate data analysis are reviewed.


This set of lecture notes grew out of work done at various times between 1984 and 1987, first in the German Federal Republic, and later and mostly in Australia. There is now a tradition in mathematics and the physical sciences of publishing work in its earlier formative phases in so-called lecture notes; this practice has not spread to psychology but the content of this particular monograph makes it apposite. Nothing final and definitive is being asserted, but a deliberate break with a tradition going back to before Fechner's foundation work in 1860 is made.

Put oversimply, the major tradition in psychophysics is one in which an environment is postulated to generate, deterministically, a random, series of events. These become stimuli for a probabilistic error-loaded organism, whose overall (i.e. externally observable) stimulus-response relationships are approximated by linear models, with superimposed Gaussian residual noise. the whole endeavour leads reasonably into psychophysical scaling, and the problems that consequently follow stem from trying to establish, both experimentally and mathematically, the regions within which the organism generates outputs that have metric properties, given that some relevant properties of the physical world may be summarised in the same framework.

This monograph quite deliberately turns the whole exercise on its head. the organism, in so far as it constitutes a single sensory channel with one- dimensional inputs, is initially treated as a nonlinear deterministic process, within a stochastic environment. Gaussian fuzziness is pushed to the outside. the mathematical assumptions used as a skeletal representation of a sensory channel are based on a difference equation of a type whose properties have only been explored in depth since the 1970's. the Fechnerian tradition in contradistinction goes back to Gauss and Laplace at the end of the 18th century. the problems of identifying when a nonlinear model fits data and when it does not are quite different from those of the more familiar general linear model, and are consequently treated de novo here. the use of time series analyses of system input-output transfer functions as a means towards identification of internal system dynamics, particularly of distinguishing random behaviour from chaotic behaviour, is noted. This is not a how-to-do-it cookbook, but the relation to earlier work by this author and others which is built on is cited, specifically in Chapters 9 and 12 where new real data are used illustratively.

Because the mathematical apparatus here is different from, and owes little to, the regression equations first introduced by Fechner, and deriving from Gauss's work in astronomy as the method of least squared residuals, it is in principle possible to treat the topic as though the tradition of classical psychophysical equations does not exist, but only that a mountain of detailed experimental data, waiting to be given some coherence and structure, lies . . .

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