Reference Systems for Brain Function

Abstract

In the last three chapters we have just hinted at the possibility of representing nerve function by sets of generalized coordinates, either following the laws of statistical mechanics (surfaces of constant energy, Gibbs ensembles), or of classical mechanics (canonical equations), or with systems of vectors as in the theory of quantum mechanics (state vectors, operators, the Schrödinger and the Heisenberg pictures). These methods would permit us to determine the future behavior of a neuronal population, provided its present state is known and the parameters introduced into the equations are reliable representatives of the state of the nervous activity. Such an abstract mathematical approach may not appeal much to the neurophysiologist, who is generally used to visualising in some way the position of his subsystem in the physical structure of the brain. Unfortunately, since there are a great number of dimensions, we have to abandon the idea of an actual pictorial or graphical representation. A functional description of the brain is possible only through an extended array of parameters, which may be thought of as constituting the coordinate axes of a space, the state of the system being a function of all the variables involved (the values of all the variables at each instant). Therefore, the position of the “image point” representing the state of the system will be, at some point within the space, continuously moving as time advances, following the minute changes of the variables’ values.