Boundary mathematics is the study of the representation and transformation of non-textual formal systems, including diagrammatic (2D), spatial (3D), iconic (pictorial) and other systems not expressed by strings of tokens.
Boundary logic amplifies Spencer-Brown's "contentless" book, Laws of Form. Boundary math (including logic, numerics, imaginaries, ...) leads to a diversity of new notational systems with new transformational properties. Here is a very short introduction to the mathematics:
|∆ boundary math|
INTRODUCTION TO THE MATHEMATICS OF BOUNDARIES How formal systems work; non-technical descriptions of boundary math; general details of container-based deduction and computation; connections to other formal systems.
BOUNDARY LOGIC Technical descriptions and details, axiom systems, and transformation tools. Studies of computation using boundary logic systems. Propositional and predicate calculus engines. Comparisons to other logic techniques.
BOUNDARY NOTATION Non-textual logic; visual, tactile, and experiential math.
SEMICONDUCTOR DESIGN TOOLS Software for logic synthesis, abstraction, library mapping, routing, and other design tasks; circuit design generator; area and delay optimization results. A lot of materials, but much of it is still trade secret.
NOVEL COMPUTATIONAL ARCHITECTURES Distinction networks, asynchronous parallel deduction, distributed computational systems, exotic hardware architectures.
BOUNDARY NUMERICS New types of numbers, a simpler numeric imaginary: log[-1].
BOUNDARY IMAGINARIES Imaginary and re-entrant forms, managing contradiction.
OTHER STUFF Culture, philosophy, exotics. Some excessively creative stuff.