Article ID: CBB001251559

Methodological Reflections on Typologies for Numerical Notations (2012)


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.

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Authors & Contributors
Snobelen, Stephen David
Guicciardini, Niccolò
Ramati, Ayval
Netz, Reviel
Tchernetska, Natalie
Saito, Ken
Studies in History and Philosophy of Science
Archive for History of Exact Sciences
Annals of Science: The History of Science and Technology
British Journal for the History of Science
Sciamvs: Sources and Commentaries in Exact Sciences
Nei Menggu Shifan Daxue Xuebao (Ziran Kexue Ban)
Princeton University Press
Yale University
Number notation; mathematical notation
Number systems
Philosophy of mathematics
Newton, Isaac
Klein, Felix
Stefan, Permskii, Saint
Ekinci, Salih Zeki
Gauss, Carl Friedrich
Time Periods
18th century
19th century
17th century
Ural Mountains region (Russia)
Académie des Sciences, Paris

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