The Mathematics of Boundaries: A Beginning

The intuitive properties of configurations of planar non-overlapping closed curves (boundaries) are presented as a pure boundary mathematics. The mathematics, which is not incorporated in any existing formalism, is constructed from first principles, that is, from empty space. When formulated as patternequations, boundary algebras map to elementary logic and to integer arithmetic. 1 De Novo Tutorial Boundary mathematics is a formal diagrammatic system of configurations of nonoverlapping closed curves, or boundary forms. Transformations are specified by algebraic equations that define equivalence classes over forms. As spatial objects, forms can be considered to be patterns, and transformations to be pattern-equations that identify valid pattern substitutions. The algebra of boundaries is novel, and is not incorporated within existing mathematical systems. Boundary mathematics provides a unique opportunity to observe formal structure rising out of literally nothing, without recourse to, ...

• Type: Conference
• Year: 2006
• Where: DIAGRAMS
• Authors: William Bricken
• Keywords: Artificial Intelligence, Boundary Mathematics, Closed Curves, DIAGRAMS 2006, Pure Boundary Mathematics