Strange loops are often characterized as "level-crossing feedback loops" that inexplicably create cycles from hierarchies. On traversing the hierarchy in an apparently monotonic manner, one is returned to the origin, often signaled by a change in context.
Some form of subspace, however, is presumed to permit the very existence of points. The very location of a point begs the question, "where?" What is the position of these points? If points are to be assigned definite locations, axes are also presumed to exist. In the graphic at upper right, the colored arrows denote the axes of extension/projection.
|"Seed, Tree, & Fruit"|
The crux of GEB is Hofstedter's proposition that strange loops are the prime material of consciousness itself.