Abstract: The properties of data series found in psychophysics are such that they are often intractable if approached simply by borrowing methodologies developed successfully in the physical sciences. At the same time such data series exhibit recurrent and identifiable qualitative features, which can be simulated by using some forms of nonlinear dynamic trajectories, particularly trajectories which are produced when two or more series are convoluted. Traditional causal and linear modelling seeks external events as the inferred stimuli for any local response patterns that exhibit replicability, when they are embedded within behavioural series that are apparently predominantly random. But such patterns may in fact be the direct consequences of the internal nonlinearity of the system. If this is so, then the only viable way to identify the underlying dynamics is to model the qualitative features with trajectories that exhibit recurrent subsequences in their phase space.
Key words: Processing, Psychophysics, Dynamics, Nonlineraity
The problems of process identification, which are common in an abstract sense to physical, physiological and psychological processes within systems, are more expediently considered within the framework of some formal definitions.
A process is a sequence of transitions between states, which has a definable terminal state, and which is replicable and controllable by the system. Any external observation of the dynamics of that process is encoded in a time series of variables; that time series may be univariate or multivariate. Each state is defined as a set of values taken uniquely by the variables of the system. The values of the variables may be numerical or symbolic. If the process is deterministic then it can be modelled by a recursive map, and is predictable in its evolution if its present state is fully known. If it is stochastic, as in the case of a random walk, then prediction of its evolution is limited to its statistical moments, usually the mean and variance. A deterministic series has an inbuilt terminal or absorbing state which arises necessarily and sufficiently from its dynamics, a stochastic series requires an additional autonomously defined terminal or barrier state beyond which it does not progress. The identification of the terminal state, such as ‘what is learned or performed’, given the initial conditions of the subject, is not sufficient to identify a process; an extensive subsample of the evolution of the process between initial and final states is necessary. It follows that a mere comparison of terminal states, as is commonly done in experimental psychology by using analysis of variance over a set of treatments and levels, is fundamentally useless for process identification.
