Subsets of Continuous Hierarchy

One of the subsets of continuous hierarchy is dynamic hierarchy. Viewed from the point of set theory (say Venn diagrams), dynamic hierarchy includes rotating sets, growing sets, shrinking sets, moving sets, jumping sets, and deforming sets. Hierarchies that continuously reform links. Hierarchies creating and destroying nodes. Loose links. Constant restructuring. Adaptable hierarchies. No ego. Only purpose. Hierarchical infrastructure that dynamic hierarchies meet get thrown into a quandry.

Another subset of continuous hierarchy is partial hierarchy. In a set theory view, the edges of the set become permeable. A member could be both in and out of a set or somewhere not quite in a set. The set boundaries may disappear leaving half of a set boundary. Some boundaries are distinct and some are non-existent, and everything in between. In the hierarchy, the edges are semipresent and are colored in gray values.

There are other subsets of continuous hierarchy that are yet to be named. One that might be considered is one where the nodes share a point instead of an edge. Another is where nodes overlap to some degree.

What seems apparent is that continuous hierarchy or continuous networking is something that has energy. Electromagnetic waves have both a particle and a wave behavior. The wave carries the particle. In continuous hierarchy, perhaps there is energy flowing between the nodes and over the edges. Perhaps in computer science, this energy may be thought of as the program counter, thread of control, or current instruction. I prefer to think of all nodes as being energized alive and operating.

All these represent primitive ideas about continuous hierarchy. The search continues.