Widom, Theodore Reed (Author)

Schlimm, Dirk (Author)

Science in Context

Volume: 25, no. 2

Issue: 2

Pages: 155-195

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.

...More Citation URI

Article
Yap, Audrey;
(2011)

Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness
(/isis/citation/CBB001024184/)

Article
Enrico Giusti;
(2017)

The Twelfth Chapter of Fibonacci's "Liber Abaci" in its 1202 Version
(/isis/citation/CBB951646036/)

Book
Wardhaugh, Benjamin;
(2010)

How to Read Historical Mathematics
(/isis/citation/CBB001020605/)

Article
Morozov, B. N.;
Simonov, R. A.;
(2008)

On the Discovery of the 14th-Century Number Notations by St. Stephan of Perm
(/isis/citation/CBB000930346/)

Article
Sarma, Sreeramula Rajeswara;
(2012)

The *Kaṭapayādi* System of Numerical Notation and Its Spread Outside Kerala
(/isis/citation/CBB001210557/)

Article
Michael Friedman;
(2020)

How to notate a crossing of strings? On Modesto Dedò’s notation of braids
(/isis/citation/CBB083323933/)

Article
Jöran Friberg;
(2019)

Three Thousand Years of Sexagesimal Numbers in Mesopotamian Mathematical Texts
(/isis/citation/CBB634644866/)

Article
Valeria Giardino;
(2018)

Tools for Thought: The Case of Mathematics
(/isis/citation/CBB112039489/)

Article
Jonah Dutz;
Dirk Schlimm;
(2021)

Babbage’s Guidelines for the Design of Mathematical Notations
(/isis/citation/CBB487959297/)

Article
Robin E. Rider;
(2020)

Equations as Unruly Objects
(/isis/citation/CBB581466291/)

Article
Dejić, Mirko;
(2014)

How the Old Slavs (Serbs) Wrote Numbers
(/isis/citation/CBB001420032/)

Thesis
Mordechai Levy-Eichel;
(2015)

"Into the Mathematical Ocean": Navigation, Education, and the Expansion of Numeracy in Early Modern England and the Atlantic World
(/isis/citation/CBB244660661/)

Article
Dipak Jadhav;
(2023)

Object-numerals as listed in Nijaguṇa Śivayogī ’s Viveka-Cintāmaṇi
(/isis/citation/CBB180449604/)

Article
Comes, Rosa;
(2006)

Notación alfanumérica griega y notaciones derivadas: uso científico-técnico
(/isis/citation/CBB001023867/)

Article
Netz, Reviel;
Saito, Ken;
Tchernetska, Natalie;
(2001)

A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 1)
(/isis/citation/CBB000102363/)

Article
Unat, Yavuz;
(2005)

Salih Zeki's Methodology in *Âsâr-i Bâkiye*
(/isis/citation/CBB000931402/)

Article
Glas, Eduard;
(2000)

Model-based reasoning and mathematical discovery: The Case of Felix Klein
(/isis/citation/CBB000110929/)

Article
Xu, Jun;
(2004)

Curt discusses Fang Zhongtong's Sisuan research and characteristics
(/isis/citation/CBB000401195/)

Article
Ramati, Ayval;
(2001)

The hidden truth of creation: Newton's method of fluxions
(/isis/citation/CBB000100557/)

Essay Review
Snobelen, Stephen D.;
(2001)

Mathematicians, Historians and Newton's *Principia*
(/isis/citation/CBB000100470/)

Be the first to comment!