Information Is Immanent Incongruence

Two combinatorial functions cross twice in the region _1..n..140._ Their slight deviations relative to each other is taken as the skeleton of an elaborate explanation model which assumes the world to be of a basic duality. The two functions are put into a context of similarity and diversity. We observe that humans’ neurology splits neuronal impulses based on the background being similar or diverse. On a similar background, we perceive ranks and sequences based on diverse properties of objects; on a background of diversity, we perceive groups of similar objects. The maximal number of diversity statements about _n_ elements of a collection deviates slightly to the maximal number of similarity statements about the same assembly. Both upper limits refer in their _f-1 _form to identical _n_, albeit with a slight mutual dis-calibration, up to _n ~ {136, 137}._ We introduce a measurement dimension: diversity/similarity. The numeric facts show that an assembly of _6 * 11 _sequenced objects has ~ _9_ times as much possible spatial variants as an assembly of _66 _objects, which facts allow for the concept of condensing information. Cycles that constitute the procedure of a reorder connect the two differing viewpoints. We introduce and tabulate the most elementary reorders and their constituent cycles and find geometric representations of different readings of _a+b=c, _which appear to picture concepts known from genetics and theoretical physics.