Numerical Notation

Abstract

This book is a cross-cultural reference volume of all attested numerical notation systems (graphic, non-phonetic systems for representing numbers), encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defies progressive, unilinear evolutionary models of change, Stephen Chrisomalis identifies five basic types of numerical notation systems, using a cultural phylogenetic framework to show relationships between systems and to create a general theory of change in numerical systems. Numerical notation systems are primarily representational systems, not computational technologies. Cognitive factors that help explain how numerical systems change relate to general principles, such as conciseness or avoidance of ambiguity, which apply also to writing systems. The transformation and replacement of numerical notation systems relates to specific social, economic, and technological changes, such as the development of the printing press or the expansion of the global world-system.

Unreliable numbers: error and harm induced by bad design can be reduced by better design

“…Interface 12: 20150685 makes studying number entry both problematic and fascinating, since it occurs in design, in use and in observation. While the development of number notations has been refined over centuries [40,41], the new field of 'interactive numbers' has yet to be developed [42].…”

The cultural origins of symbolic number.

“…An abundance of multibase systems have also been studied in Papua New Guinea and Oceania (Owens, 2001; Owens & Lean, 2018), for instance the common 2-5-20 cycle, where counting proceeds: 1, 2, 2 + 1, 2 + 2, 5 (often one “hand”), 5 + 1, 5 + 2, 5 + 2 + 1, 5 + 2 + 2, 5 + 5, and so on, up to a new base of 20 (often one “man”). Even systems of finger counting show a great deal of diversity (Bender & Beller, 2012), as do numerical notation systems (Chrisomalis, 2009b).…”

“…However, the relation between number and culture is not found in a simple unilineal social development of number concepts (Donohue, 2008), as some 19th-century theorists believed (e.g., Crawfurd, 1863). Epps et al (2012) for instance have argued that hunter-gatherer and agriculturalist modes of social organization are not good predictors of number system development, and in the development of written numerical systems, Chrisomalis (2009b) provides evidence for a multilineal, rather than unilineal evolution. Yet the greater elaboration of number systems is, in general, related to greater sociocultural complexity (Chrisomalis, 2009b; Divale, 1999; Nissen et al, 1993; Overmann, 2016; Robson, 2008; Schmandt-Besserat, 1978).…”

“…Epps et al (2012) for instance have argued that hunter-gatherer and agriculturalist modes of social organization are not good predictors of number system development, and in the development of written numerical systems, Chrisomalis (2009b) provides evidence for a multilineal, rather than unilineal evolution. Yet the greater elaboration of number systems is, in general, related to greater sociocultural complexity (Chrisomalis, 2009b; Divale, 1999; Nissen et al, 1993; Overmann, 2016; Robson, 2008; Schmandt-Besserat, 1978). Sociocultural complexity here refers largely to matters of material culture, hierarchical division, socioeconomic stratification, population density, and the production and management of surplus (e.g., for ceremonial feasting; Hayden & Villeneuve, 2011).…”

“…In contrast, we argue that symbolic number and counting fail all of the natural predictions (i)–(vi) of biological determinism. The cultural history of mathematics shows that, large, exact, symbolic number is cognitively difficult for humans to create, the product of a long cross-cultural history (Chrisomalis, 2009b; Damerow, 2015; Ifrah, 2000; Joseph, 1987) and that modern conceptions of number are far from universal across human groups. The picture that emerges instead from the ethnographic literature reveals a diversity of culturally contingent approaches to problems of quantity, which are constructed according to local needs, perceptions, practices, and history (Beller et al, 2018; Crossley, 2007; Dixon & Kroeber, 1907; Hymes, 1955; Owens & Lean, 2018; Robson, 2008; Wolfers, 1971).…”