Life, information theory, and topology

Abstract

The information content of an organism determines to a large extent its ability to perform the basic vital functions: selection of food, breaking up of the food molecules into appropriate parts, selection of those parts, and their assimilation. The information content needed is very large and requires a sufficiently large complexity of the organism. The information content of an organism is largely determined by the information content of the constituent organic molecules. The information content of the latter is in its turn determined by the number of physically distinguishable atoms or radicals of which the molecule is composed. The different arrangements of atoms in a molecule are represented by the structural formula, which is basically a graph. It is shown that the topology of this graph also determines to a large extent the information content. Different points of a graph may be physically indistinguishable; in general, however, they are different in regard to their topological properties. A study of the relations between the topological properties of graphs and their information content is suggested, and several theorems are demonstrated. A relation between topology and living processes is thus found also on the molecular level.