Last month, at the Society for Anthropological Sciences annual meeting in Charleston, SC, I organized a panel of some really interesting material on the broad topic of numeration. I want to take this opportunity (again) to thank all the presenters for their attendance and hard work. The abstracts (as also published in the conference program) were as follows:
Toward a cognitive, historical, linguistic anthropology of numerals
Stephen Chrisomalis (Wayne State University)
For over a century, the study of numeration, number systems and allied topics has been a key part of the comparative study of thought, language, and culture. The anthropology of numbers and mathematics has traditionally been a locus for unilinear evolutionary thought linked to notions of primitivity. The papers in this panel constitute a call for a culturally-grounded cognitive science of numeration within four of the disciplines of cognitive science (anthropology, linguistics, philosophy, and psychology).
Recent research in language evolution, linguistic relativity, and cultural aspects of mathematical cognition draw attention to the need for anthropologists to re-engage with this new agenda. First, the cross-cultural study of numerals allows the investigation and evaluation of universal and particular aspects of numeration and their relationship with social organization. Because numerals have multiple modalities (e.g., verbal, graphic, gestural), examining patterns in number systems beyond linguistics allows us to evaluate to what extent number concepts can be separated from language, including universal grammar. Finally, just as the cognitive anthropology of plant and animal taxonomy contributes to ecological and environmental anthropology, the cognitive anthropology of numerals and mathematics underpins economic anthropology and the anthropology of science.
Spatial-numeric associations in literates and illiterates
Samar Zebian (Lebanese American University, Beirut Lebanon)
Several independent studies have reported a cognitive association between small numbers and the left side of space and larger numbers andthe right side of space among individuals who read and write from left-to-right (SNARC effect). These associations are reversed for individuals who read and write from right-to-left. The SNARC effect has widely been taken as evidence that numbers are conceptualized as points along a mental number line, however there is growing evidence that this systematic spatial performance bias related to writing directionality is an instance of strategic processing rather than a reflection of inherent spatial attributes of numbers. In an attempt to explain the “deeper” origins of these associations researchers are examining the linkages between number and finger counting. The current study examines whether finger counting practices reveal consistent spatial-numeric associations and whether there are any spillover effects to other tasks that involve object sorting and counting and other non-counting but quantitative tasks such as line bisection and speeded parity judgment. If, in fact, finger counting practices and not the directionality of writing set up spatial-numeric associations than we should be able to observe the same type of spatial biases in literates and illiterates. Preliminary evidence suggests that the finger counting practices of literates and illiterates are not same and furthermore that the spatial biases found in finger counting are not observed across tasks.
Zero’s beginnings: the Mayan case
John Justeson (SUNY, Albany)
This paper addresses linguistic and (Mayan) historical evidence concerning the origins of a numerical concept of zero. Comparative linguistic evidence suggests that zero is not part of basic numerical cognition; rather, it develops out of computing practices of mathematical specialists. Specifically, while zero is often assumed to be prerequisite to the invention of positional notation, it seems on the contrary to emerge as a notational device within such systems. This is clearly the case in Mesoamerica. A system of place-value notation arose in Guatemala and Mexico among Mayans and epi-Olmecs by 36 BCE, with no symbol corresponding to a zero coefficient. Although data is limited, circumstantial evidence is consistent with the following scenario for the emergence of a numerical zero: Mayan calendar specialists developed discourse practices, associated with calendrically-timed ritual events, that used the word “lacking”; the associated dates were represented in a new, non-positional system of notation, which replaced positional notation except in calculating tables; the sign for “lacking” was transferred from the new notation into these tabular positional notations; as a side effect of the algorithms that specialists used to add and subtract positional numerals, the “lacking” symbol was reinterpreted numerically.
Methodological reflections on typologies for numeral systems
Theodore R. Widom and Dirk Schlimm (McGill University)
Past and present societies worldwide 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. In the present paper we provide a general framework
within which the efficacy of these typologies can be assessed relative to certain desiderata. Using this framework, we discuss the two influential typologies of Zhang & Norman and Chrisomalis, and present a new typology which takes as its starting point the principles by which numeral systems represent multipliers (the principles of cumulation and cipherization), and
bases (those of integration, parsing, and positionality). We argue with many different examples that this provides a more refined classification of numeral systems than the ones put forward previously. We also note that the framework can be used to assess typologies not only of numeral systems, but of many domains.
Social relationships as a lexical source for numeral terms in Amazonia
Cynthia Hansen and Patience Epps (The University of Texas at Austin)
Due to the relatively high degree of etymological transparency found in the numeral systems of Amazonia, it is possible to see the range of lexical sources from which the numeral terminology emerges. In this paper, we present the range of strategies used to create numeral terms below 5, based on an extensive survey of the numeral systems of close to 200 Amazonian languages conducted by the authors. More specifically, we discuss a strategy that is well-attested in Amazonia but that is not attested elsewhere in the world: a ‘relational’ strategy where terms for 4 (and sometimes 3-10) are built using a social relationship term, such as ‘sibling’ or ‘companion’. We propose that this strategy mirrors a gestural counting strategy found throughout the region where fingers are grouped in pairs.
Cultural variation in numeration systems and their mapping onto the mental number line
Andrea Bender and Sieghard Beller (University of Freiburg)
The ability to exactly assess large numbers hinges on cultural tools such as counting sequences and thus offers a great opportunity to study how culture interacts with cognition. To obtain a more comprehensive picture of the cultural variance in number representation, we argue for the inclusion of cross-linguistic analyses. In this talk, we will briefly depict the specific counting systems of Polynesian and Micronesian languages that were once derived from an abstract and regular system by extension in three dimensions. The linguistic origins, cognitive properties, and cultural context of these specific counting systems are analyzed, and their implications for the nature of a (putative) mental number line are discussed.