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.
