505.10 Euler: Minimum Aspects of Pattern

505.101 Euler said that we are dealing in pattern. Mathematics is pattern, and there are irreducible aspects of pattern. That is, the patterns represent events. A line is a unique kind of pattern. If I have two lines, where the two lines cross is distinctly different from where the two lines do not cross. Euler called this the vertex, the convergence. He saw this as absolute pattern uniqueness.

505.11 Euler showed that all optical experiences that we can pattern or form are composed exclusively of three patterning elements: lines, vertexes, and areasor trajectories, crossings, and openings, as they are known in synergetics. These incontrovertible minimum aspects of pattern are all that is necessary to analyze and inventory all parts of all optically apprehended patterns as well as of all whole patterns. And Euler disclosed three algebraic formulae characterizing the constant relative-abundance relationships of these three fundamental topological elements in all patterns.

505.12 All happening patterns consist of experience recalls. The recallable ingredients of experiences consist inherently of paired-event quanta of six-vectored positive and negative actions, reactions, and resultants.