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
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Andrea Bender & Sieghard Beller (2012). Nature and Culture of Finger Counting: Diversity and Representational Effects of an Embodied Cognitive Tool. Cognition 124 (2):156-182.
Andrea Bender, Dirk Schlimm & Sieghard Beller (2015). The Cognitive Advantages of Counting Specifically: A Representational Analysis of Verbal Numeration Systems in Oceanic Languages. Topics in Cognitive Science 7 (4):552-569.
Dirk Schlimm (2013). Conceptual Metaphors and Mathematical Practice: On Cognitive Studies of Historical Developments in Mathematics. Topics in Cognitive Science 5 (2):283-298.
Andrea Bender & Sieghard Beller (2016). Current Perspectives on Cognitive Diversity. Frontiers in Psychology 7.
Stephen Chrisomalis (2013). Constraint, Cognition, and Written Numeration. Pragmatics and Cognition 21 (3):552-572.
Similar books and articles
M. J. Cresswell (2006). Arabic Numerals in Propositional Attitude Sentences. Analysis 66 (289):92–93.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Elizabeth S. Spelke (2010). Core Multiplication in Childhood. Cognition 116 (2):204-216.
Marinella Cappelletti & Lisa Cipolotti (2006). Unconscious Processing of Arabic Numerals in Unilateral Neglect. Neuropsychologia 44 (10):1999-2006.
Charles Sayward (2000). Remarks on Peano Arithmetic. Russell 20 (1):27-32.
Mojżesz Presburger & Dale Jabcquette (1991). On the Completeness of a Certain System of Arithmetic of Whole Numbers in Which Addition Occurs as the Only Operation. History and Philosophy of Logic 12 (2):225-233.
M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.
Added to index2009-01-28
Total downloads60 ( #79,574 of 1,941,073 )
Recent downloads (6 months)3 ( #272,622 of 1,941,073 )
How can I increase my downloads?