Modeling ancient and modern arithmetic practices: Addition and multiplication with Arabic and Roman numerals
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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In B. C. Love, K. McRae & V. M. Sloutsky (eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society. Cognitive Science Society 2097--2102 (2008)
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.
|Keywords||Numerals Cognitive modelling Roman numerals|
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