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Methodological Reflections on Typologies for Numerical Notations

Published online by Cambridge University Press:  24 April 2012

Theodore Reed Widom  and
Dirk Schlimm
Theodore Reed Widom
Affiliation:
McGill University E-mail: theodore.widom@mail.mcgill.ca
Dirk Schlimm
Affiliation:
McGill University E-mail: dirk.schlimm@mcgill.ca
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Argument

Past and present societies world-wide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. The present paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework to discuss the two influential typologies of Zhang & Norman and Chrisomalis. Following this, a new typology is presented that takes as its starting point the principles by which numerical notations represent multipliers (the principles of cumulation and cipherization), and bases (those of integration, parsing, and positionality). Many different examples show that this new typology provides a more refined classification of numerical notations than the ones put forward previously. In addition, the framework provided here can be used to assess typologies not only of numerical notations, but also of many other domains.

Information

Type
Research Article
Information
Science in Context , Volume 25 , Issue 2 , June 2012 , pp. 155 - 195
Copyright
Copyright © Cambridge University Press 2012

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