You do not currently have permission to view the full text for this document. Please sign in to an account with an active subscription or contact support.
Biomathematics is a discipline which applies mathematics to solve biomedical questions. Several journals, such as the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, publish mathematical models of a broad variety of physiological and biochemical phenomena including topics such as kidney function, heart action, genetic phenomena, and psychological events. I am a medical doctor whose career has been in the field of biomathematics. Some of my work has involved the mathematical modelling of human psychomotor behaviour (Barnwell et al 1973; Albanese 1974; Albanese et al 1974). Starting from this work and prompted further by discussions with my psychiatrist wife, I have recurrently asked over the years whether mathematical structures exist which might model, or serve as analogues to, normal and pathological higher mental functioning. Reading and learning across a spectrum of approaches including Freudian theory, object relations, Rogerian theory and cognitive psychology, I had tentatively concluded that mathematical structures were not currently available for detailed and useful modelling of important elements of psychopathological and psychotherapeutic processes; or, at least, that my mental abilities were not up to the task of such modelling endeavours. Thus, it was with a significant degree of pessimism and scepticism that I first heard Dr Robert Langs' suggestion that the communicative exchange occurring during the psychotherapeutic process might well be modelled using the mathematics of nonlinear systems theory. Extended discussions with Dr Langs and study of selected pieces from his writings has led me to believe that Dr Langs is correct regarding the applicability of nonlinear systems mathematics (Langs 1980, 1985, 1986).
In this article I attempt to describe briefly nonlinear systems theory and thereby to show its plausible relationship to the psychotherapeutic process. I will further support the applicability of this theory by displaying a