The Cognitive Advantages of Counting Specifically: A Representational Analysis of Verbal Numeration Systems in Oceanic Languages

Abstract

The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences. These sequences constitute systems with distinct structural properties, the cross-linguistic variability of which has implications for number representation and processing. Such representational effects are scrutinized for two types of verbal numeration systems-general and object-specific ones-that were in parallel use in several Oceanic languages (English with its general system is included for comparison). The analysis indicates that the object-specific systems outperform the general systems with respect to counting and mental arithmetic, largely due to their regular and more compact representation. What these findings reveal on cognitive diversity, how the conjectures involved speak to more general issues in cognitive science, and how the approach taken here might help to bridge the gap between anthropology and other cognitive sciences is discussed in the conclusion.

The Power of 2: How an Apparently Irregular Numeration System Facilitates Mental Arithmetic

“…Bender, S. Beller / Cognitive Science 41 (2017) numeme: X = rogo'uru (10), C = rau (100), K = takau (10), P = paua (20), T = tataua (40), and V = varu (80). It should be noted here that this is not (reliably) so in English, which is irregular in this regard: "ten" and "two" in English yields not "ten-two," but "twelve" (for implications of this irregularity, see, for example, Beller & Bender, 2011;Bender et al, 2015). 2 Additions (and multiplications) with 10 (X) are part of the classical addition (and multiplication) tables and are therefore also integrated in Table 2; the same holds for addition with 100 (C) in Table 3A and for addition with 80 (V) in Table 3B.…”

“…Nonetheless, in any case, none of these strategies gets by with fewer than three stepsand this is substantially more than the transformations required for the mixed system (for a more detailed account of the role that memory access may play for these steps, see Bender et al, 2015). S10 thus requires three distinct steps (if we disregard joining), and the same is true for A10 (v.ii).…”

“…This latter property has not been considered thus far, as it has been dealt with in some detail elsewhere (Beller & Bender, 2005;Bender et al, 2015). This latter property has not been considered thus far, as it has been dealt with in some detail elsewhere (Beller & Bender, 2005;Bender et al, 2015).…”

“…Their familiarity with a decimal place-value system, and specifically the Hindu-Arabic digits, however, inevitably affects how they represent numbers (Dehaene, 1992). As detailed in Bender et al (2015), the theoretical models derived from such research are thus necessarily constrained and cannot be assumed to account for the arithmetic abilities and strategies of people not familiar with this notational system.…”

Diversity as Asset

“…The construal of numeration systems, for instance, is generally based on a limited set of key properties, yet the concrete instantiations of these properties and their combination may vary substantially even in related languages—numbers are represented in a language‐specific format. These differences in representational format, in turn, can be assumed to affect the processing of numerical information, even if only as a matter of degree rather than kind, for instance, by facilitating some types of algorithmic processes relative to other representational formats (Bender, Schlimm, & Beller, ). Likewise, the subject of body part taxonomies is naturally the same for all mankind, and both the visual and embodied perception of the human body set strong constraints on which discontinuities should be regarded as relevant in principle.…”