Abstract
Papers on diagrammatic reasoning often begin by dividing marks on paper into two basic classes: diagrams and sentences. While endorsing the perspective that a reasoning episode can be diagrammatic or sentential, I will give an overview of recent evidence suggesting that apparently symbolic expressions in algebra and arithmetic are frequently treated as diagrammatic or even pictorial depictions of objects and events—events that occur not in the content of the expression, but within the notation itself. This evidence suggests that algebra is sometimes less a matter of rules and abstract syntax, and more a matter of constraints on the physical behavior and part-whole structure of notational things: an idiosyncratic notational physics, whose laws constrain the structure of proofs. These considerations suggest that whether some marks are a diagram depends on exactly how a user engages them.
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Landy, D. (2010). Toward a Physics of Equations. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds) Diagrammatic Representation and Inference. Diagrams 2010. Lecture Notes in Computer Science(), vol 6170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14600-8_16
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DOI: https://doi.org/10.1007/978-3-642-14600-8_16
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