Proceedings of the Annual Meeting of the Cognitive Science Society

In this paper, we study the representational properties of numeration systems. W e argue that numeration systems are distributed representa- tions—representations that are distributed across the internal mind and the external envi- ronment. W e analyze number representations at four levels: dimensionality, dimensional repre- sentations, bases, and symbol representations. The representational properties at these four levels determine the representational efficien- cies of numeration systems and the performance of numeric tasks. From this hierarchical struc- ture, we derive a cognitive taxonomy that can classify most numeration systems.