A comparison of set-theoretical and graph-theoretical approaches in topological biology

Abstract

Two somewhat different approaches to topological biology have been developed in recent years. The latest, set-theoretical approach leads rather immediately to a number of conclusions which are verified experimentally. It also predicts a number of new biological relations. The older, graph-theoretical approach does not lead directly to those conclusions but suggests a number of combinatorial relations between number of organs and number of cell types. Such suggestions are absent from the set-theoretical approach. It is shown that the above-mentioned combinatorial relations are independent of the graph-theoretical method proper and can be introduced into the set-theoretical approach through the addition of an independent postulate.

A possible addition to the principle of biotopological mapping is suggested, which brings into focus the relations between the organism and its individual organs and which has a predictive value.