Introduction to Boundary Math

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Over the last two decades I've written many descriptions of boundary math and boundary logic. The concepts of these systems have been particularly difficult to communicate, so I've tried talks, seminars, academic publications, business memos, computer implementations, popular articles, and just about everything else I could think of.

What's so difficult? The ideas that rational and formal thought can exclude false ideas by not pointing to them; that it is not OK to call nothing something (like "nothing"); that group theory is not the only way to organize math; that clear mindedness means empty mindedness.

boundary math

∆ introduction
boundary logic
circuit design

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When rational thought is treated as an accumulation of facts, it becomes complicated; when it is treated as an active forgetting of irrelevancies, it becomes simple. These ideas can be expressed symbolically, but only by using representational forms of a higher dimension than strings, that is, by using containers.

Here is a distillation of the rules of formal symbol systems (following Spencer Brown):


SIMPLE DESCRIPTIONS –– Several ways to think about the mathematics of boundaries. The technical details about using boundaries for computation are in the Boundary Logic section.

DIAGRAMMATIC FORMAL SYSTEMS –– recent work (2005) inspired by C.S. Peirce's Alpha Existential Graphs. The idea is to take spatial structure seriously as mathematical form.

CONNECTIONS TO OTHER MATHEMATICAL SYSTEMS –– The relationship of boundary math to other mathematical systems. Symbolic but generally not technical exploration.