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Iconic, diagrammatic, and spatial mathematical forms not only look different, they support new varieties of transformation and new ways to envisage computation, proof and rationality. Calculation by following paths, walking down stairs, opening and closing doors, and stacking blocks is quite different than juggling symbol strings. The main ideas are in this paper published paper (with material taken from Nonsymbolic Logic below):
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Syntactic Variety was presented at Diagrams 2006. Here are some versions of the presentation:
In Non-Symbolic Logic, I set out to write a monograph without words. The first piece of this unfinished work is a quick cut-and-paste of content; the second is a chapter (XVII) showing non-symbolic proof examples in eight non-string notations. Boundary Notation is Jeff James' experiments with spatial algebra.
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