TOWARD AN ALGEBRAIC GNOSEOLOGY

Abstract

In this paper we present a functional model of a portion of a mammalian brain. That is, a model that both simulates some of the anatomo-functional properties characterizing large pieces of the nervous tissue and imitates some of the, we hope fundamental, functional aspects of a whole brain. To test our picture we propose also some applications to an, admittedly, simplified universe. To aid in our task we shall use a version of a data-flow computer similar to the one previously introduced. Its associated language, at a syntactic level, has the algebraic structure of a free group. This allows us to systematically investigate the possibility to exploit the equations in such kind of structure. In other words, the free group is a kind of metaenvironment into which we can obtain procedures, operating upon procedures, via the juxtaposition and the inverse rules defined within the algebraic structure. To arrive at the formulation of our model, we begin with a discussion of the relevant data and notions about the structure and functioning of some nerve ganglion and of its ultimate component, the neuron. To simplify our exposition we refer almost exclusively to the most recent literature, but the reader is strongly urged to also look at the other works listed. In any case, we hope to have selected all the basic notions so that our picture of a functioning brain can still be acknowledged as a fair one. In conclusion, we are well aware that the model we outline here is probably nearer to the Lull's turning wheels than to reality.