Base structures across lexical and notational numeral modalities

The base concept in number systems is realized differently across multiple representational modalities-frameworks that incorporate sensory channel, medium of expression and semantic structures into integrated semiotic systems. Because these three factors are interdependent, a much closer assessment of how they jointly affect numerical representations is sorely needed. Number words (lexical numerals) and graphic notations (numerical notations) are the two best-attested numerical modalities cross-culturally. Users may choose between one or the other, or combine the two together as hybrid expressions (as in 1.2 million). Many features of numerical systems, such as base-5, sub-bases, irregular base structures and iteration, vary both cross-culturally and across modalities. These differences are not merely typological or arithmetical but derive from the integration of channel, medium and structure as mediated through human cognition. Comparing these two modalities' constraints and affordances for ambiguity avoidance, phrase ordering and conciseness thus helps achieve a better understanding of the range of human numerical expressions and their effects.This article is part of the theme issue 'A solid base for scaling up: the structure of numeration systems'.