The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the (...) universalist/particularist dichotomy. In place of strictly innatist perspectives on mathematical cognition, a model is proposed that invokes domain-specific and notationally-specific constraints to explain patterns in numerical notations. The analysis of exceptions to cross-cultural generalizations makes the study of near-universals highly productive theoretically. The cross-cultural study of patterns in written numbers thus provides a rich complement to the cognitive analysis of writing systems. (shrink)

The world’s diverse written numeral systems are affected by human cognition; in turn, written numeral systems affect mathematical cognition in social environments. The present study investigates the constraints on graphic numerical notation, treating it neither as a byproduct of lexical numeration, nor a mere adjunct to writing, but as a specific written modality with its own cognitive properties. Constraints do not refute the notion of infinite cultural variability; rather, they recognize the infinity of variability within defined limits, thus transcending the (...) universalist/particularist dichotomy. In place of strictly innatist perspectives on mathematical cognition, a model is proposed that invokes domain-specific and notationally-specific constraints to explain patterns in numerical notations. The analysis of exceptions to cross-cultural generalizations makes the study of near-universals highly productive theoretically. The cross-cultural study of patterns in written numbers thus provides a rich complement to the cognitive analysis of writing systems. (shrink)

All sufficiently large functional notations (ideographic or otherwise) are composites of discrete, structured elements (e.g., phonemes, morphemes, numerals). We must consider not only the modality but also the structure of the existing, workable ideographic/semasiographic systems we know (e.g., musical and numerical notation) to establish the cognitive limitations militating against humans memorizing and standardizing domain-general ideographies that would parallel written language.