Toward a mathematical description of the grey substance of nervous systems

A striking par t icular ly of the biophysics of brains is t h a t it deals with macroscopical organs, well accessible to s t ructural and funct ional analysis, a b o u t which a great deal of informat ion is collected in the l i terature but l i t t l e i f any s a t i s f ac to ry unders tanding of the central problems has been obtained. The search for be t t e r resolution in techniques developed recently, such as electron microscopy or electrical recording f rom single nerve cells has shown only too clearly tha t li t t le can be gained b y pushing the analysis to smaller orders of magni tude. The main question, how a bra in does per form the remarkab le functions which are often so difficult to imi ta te b y machine is obviously related to the high degree of complexi ty of the s t ructure of nerve cell aggregates (in the so-called grey substance) and to the equally high degree of functional organizat ion which is appa ren t in them. This organized comp lex i ty poses novel problems to analysis. The divergent descriptions of the brains, ranging f rom introspect ive psychology to compara t ive n e u r o a n a t o m y or the physiology of synapses would still be even wi thout the hope of a comm o n language, had it not been for recent a t t emp t s to formula te theories abou t the bra in in a rigorous form which, potential ly, embody all t ha t can be said abou t brains. I t is to these theories, as well as to some aspects of the brain which have not ye t been buil t into the theories tha t we shall devote our a t ten t ion here.