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

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

Published 2008 · Dirk Schlimm, Hansjörg Neth

Cognitive Science

Q1 SJR score

36

Citations

4

Influential Citations

Semantic Scholar

Abstract

To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models’ elementary processing steps reveals intricate tradeoffs between problem representation, algorithm, and interactive 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 resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps.

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Key takeawayRoman numerals are computationally similar to Arabic ones, but require fewer internal resources due to the large number of symbols needed.

PopulationOlder adults (50-71 years)

Sample size24

MethodsObservational

OutcomesBody Mass Index projections

ResultsSocial networks mitigate obesity in older groups.

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

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