A Cognitive Taxonomy of Numeration Systems

In this paper, we study the representational properties of numeration systems. We argue that numeration systems are distributed representationsÑrepresentations that are distributed across the internal mind and the external environment. We analyze number representations at four levels: dimensionality, dimensional representations, bases, and symbol representations. The representational properties at these four levels determine the representational efficiencies of numeration systems and the performance of numeric tasks. From this hierarchical structure, we derive a cognitive taxonomy that can classify most numeration systems