Return to Postsymbolism

Today Mathematics remains symbolic while other communication media have evolved into visual and interactive experiences.

We write on lines of paper but what of the communication of artists and sculptors and film-makers? We speak in a linear flow of words, but what of the non-linear flow of music and poetry and dance? We read books that display strings of tokens but what of the display of illustrations and photographs and videos and websites? Our digital computation tools can render both lines of text and dynamic images but that which is encoded within huge strings of binary digits has no knowledge of context or environment. Symbolic computation cannot make a distinction, cannot have an idea; it can neither know nor deceive itself.3

Although symbolic mathematics may be eternal, the context, meaning, relevance, interpretation and worthiness of any aspect of mathematical symbolism is involuted by physical time and by cultural change.

**Belief in mathematics** is *not* eternal. Indeed a theme of postsymbolism is that formal decisions and commitments made in one era can in a later era become dubious. Hilbert sought to design a mathematics that supported entirely its own validity, without reference to the context that contains it. Prior to our modern understanding of cybernetics, ecology and embodiment, Hilbert’s dream of metamathematics was a great improvement that literally laid the groundwork for the computational age. But by design metamathematics cannot be *relevant*. Symbols are necessarily obscured, obliterated, by their meaning. Formal symbol systems are designed to deceive. There is no there there.

More accurately what remains is metaphysiscs, an appeal to semantic magic that connects symbolic structure to Experience. We provide the Magic by disembodying cognition.

Digital technology has spurred an evolution in the representation and acquisition of mathematical knowledge. Mathematics is shifting to visual rather than textual forms of expression. Venn diagrams, Feynman diagrams, diagrammatic reasoning, cellular automata, fractals, knot theory, string theory, category theory, silicon circuit design; each of these fields relies upon the iconic representation of formal systems. Like geometry these fields can be seen as addressing inherently multidimensional concepts. Formalism is escaping its symbolic constraints.

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Bricken, Iconic Arithmetic Volume III: The Structure of Imaginary And Infinite Forms, pdf , p. 376–377.