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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:
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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.
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