Organic Mathematics: On the Extension of Logics from Physical Atoms to Cellular Information Processes

Abstract

Formally, cellular information processing requires mathematical forms of representation of parts of the whole. Several types of mereological operands, co-operands, and operators are necessary to embed the symbolic meanings. The common source of propositions is the atomic numbers, taken as both (measurable) physical objects and mathematical objects. The atomic numbers serve as source of the novel notation for organic mathematics. The historical scientific basis for the notation is described in terms of the electrical particles (abstractly defined as cardinal and ordinal numbers). The regular order of atomic numbers as diagrams define the radix attributes of the perplex number system. A triad of mathematical constructs built from the perplex numerals include quantum mechanics, the table of elements, and molecular biology. The radix of the hybrid logic of biological information processing includes forms of both copulative and predicative propositions on the attractive and repulsive attributes of electrical particles.