1.3
Boundary Math Notations
home page

Usually the notation, or syntax, of a formal system does not interact with the meaning, or semantics, of the system. This is not the case with void-based representations since the syntax highlights (i.e. draws a picture of) the semantics of void-based computational forms. Each notational variety is formally the same as the others, but each shows us a new way of thinking about mathematics and logic, a new way of thinking about thinking. Here's the general argument:

WEAK WORDS
boundary math

introduction
boundary logic
∆ notation
circuit design
architectures
numerics
imaginaries
culture

site structure

NON-SYMBOLIC LOGIC –– Dozens of notations for logic: textual, iconic, spatial. Spatial algebra.

The heart of the technical issue is whether or not a graph and a map are the same data structure (they are not, although they are isomorphic in conventional string notations). One important difference is the location of our Point-of-view: Containers permit viewing from the inside as well as from the outside. Words do not have an inside. The last two pieces are experiments with boundary notations.

REPRESENTATIONS OF BOUNDARY LOGIC (overview)
GRAPH-MAP ISOMORPHISM
POINT OF VIEW
BOUNDARY LOGIC AS ENCRYPTION PUZZLE
CYCLIC STRING NOTATION