SIAM-AMS Proceedings Volume 13 1981
1. Introduction. Several of the best physicists of the last half of the nineteenth century were also distinguished psychologists or physiologists. The contributions of Helmholtz, Maxwell, and Mach to perception are notable examples of this productive interdisciplinary activity ( Boring [ 1950], Koenigsberger [ 1906], Campbell and Garnett [ 1882], Ratliff [ 1965]). Why then did not interdisciplinary studies, based on these inspiring successes, flourish at the beginning of the twentieth century?
One reason lies in the nature of psychophysiological phenomena. The mathematics of traditional physics has been centered in linear and stationary concepts, whereas the data of psychophysiology are often nonlinear and nonstationary. The great revolutions of twentieth century physics were supported by nineteenth century mathematics, but the emergent concepts of psychophysiology, from the very outset, lead to new mathematics. We seem to be experiencing the type of scientific revolution wherein new intuitive physical concepts and new mathematics must both be simultaneously developed, each fertilizing the other. Such scientific developments bring with them special challenges, but also special intellectual rewards.
In this article, I shall discuss nonlinear and nonstationary concepts that arise from consideration of some basic questions about brain design, and I will indicate how the answers help to unify several of the contributions reported elsewhere in the book. These questions include: How can an organism's adaptive mechanisms be stable enough to resist environmental fluctuations which do not alter its behavioral success, but plastic enough to change rapidly in response to environmental demands that do alter its behavioral success? How is a balance between stability and adaptability achieved in a nonstationary environment? More simply expressed, how do internal representations of the environment
1980 Mathematics Subject Classification. Primary 92A25; Secondary 92A09.
© 1981 American Mathematical Society____________________