Locality and globality: Estimations of the encryption collectivities

Abstract

In this paper we try to define a collectivity, to model and to measure it. Because N. Bourbaki names ”collectivizing relation” the relation defining a set, we name collectivities only the sets selected or built by the help of the relations. The orthogonal interconnections model very well the collectivities. The behavior (structural self-organization) around the origin is different for homogenous and non-homogenous interconnections. How can we measure this behavior? A way is by locality and globality. The locality measures analytically by neighborhoods, neighborhood reserves, Moorereserves and synthetically by diameters, degrees, average distances. The globality is the behavior of an interconnection around a property. The globality vs. symmetry measures by the compactity, efficiency and interconnecting filling. The locality and the globality are among primary manifestations of the self-organization. In this way, collectivities modeled by self-organizing interconnections can contribute to changing our fundamental view of computers by trying to bring them nearer to the nature.