Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals

To analyze the task of mental arithmetic with external repre-sentations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numer-als. This demonstrates that Roman numerals are not only infor-mationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models ’ elementary processing steps reveals intricate trade-offs between problem representation, algorithm, and interac-tive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. While symbolic computation with Roman numerals requires fewer internal re-sources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps