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. (shrink)

Classical cognitive science was launched on the premise that the architecture of human cognition is uniform and universal across the species. This premise is biologically impossible and is being actively undermined by, for example, imaging genomics. Anthropology (including archaeology, biological anthropology, linguistics, and cultural anthropology) is, in contrast, largely concerned with the diversification of human culture, language, and biology across time and space—it belongs fundamentally to the evolutionary sciences. The new cognitive sciences that will emerge from the interactions with the (...) biological sciences will focus on variation and diversity, opening the door for rapprochement with anthropology. (shrink)

It is widely assumed that human learning and the structure of human languages are intimately related. This relationship is frequently suggested to derive from a language-specific biological endowment, which encodes universal, but communicatively arbitrary, principles of language structure (a Universal Grammar or UG). How might such a UG have evolved? We argue that UG could not have arisen either by biological adaptation or non-adaptationist genetic processes, resulting in a logical problem of language evolution. Specifically, as the processes of language change (...) are much more rapid than processes of genetic change, language constitutes a both over time and across different human populations, and, hence, cannot provide a stable environment to which language genes could have adapted. We conclude that a biologically determined UG is not evolutionarily viable. Instead, the original motivation for UG arises because language has been shaped to fit the human brain, rather than vice versa. Following Darwin, we view language itself as a complex and interdependent which evolves under selectional pressures from human learning and processing mechanisms. That is, languages themselves are shaped by severe selectional pressure from each generation of language users and learners. This suggests that apparently arbitrary aspects of linguistic structure may result from general learning and processing biases deriving from the structure of thought processes, perceptuo-motor factors, cognitive limitations, and pragmatics. (shrink)

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. 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. (shrink)

Is the application of more than one number system in a particular culture necessarily an indication of not having abstracted a general concept of number? Does this mean that specific number systems for certain objects are cognitively deficient? The opposite is the case with the traditional number systems in Tongan, where a consistent decimal system is supplemented by diverging systems for certain objects, in which 20 seems to play a special role. Based on an analysis of their linguistic, historical and (...) cultural context, we will show that the supplementary systems did not precede the general system, but were rather derived from it. Especially when notation is lacking, having such supplementary systems can even yield cognitive advantages. In using larger counting units, they both abbreviate counting and expand the limits of the general system, thus facilitating the cognitive task of mental arithmetic. (shrink)

Anthropology and the other cognitive science (CS) subdisciplines currently maintain a troubled relationship. With a debate in topiCS we aim at exploring the prospects for improving this relationship, and our introduction is intended as a catalyst for this debate. In order to encourage a frank sharing of perspectives, our comments will be deliberately provocative. Several challenges for a successful rapprochement are identified, encompassing the diverging paths that CS and anthropology have taken in the past, the degree of compatibility between (1) (...) CS and (2) anthropology with regard to methodology and (3) research strategies, (4) the importance of anthropology for CS, and (5) the need for disciplinary diversity. Given this set of challenges, a reconciliation seems unlikely to follow on the heels of good intentions alone. (shrink)

This paper reviews the uneven history of the relationship between Anthropology and Cognitive Science over the past 30 years, from its promising beginnings, followed by a period of disaffection, on up to the current context, which may lay the groundwork for reconsidering what Anthropology and (the rest of) Cognitive Science have to offer each other. We think that this history has important lessons to teach and has implications for contemporary efforts to restore Anthropology to its proper place within Cognitive Science. (...) The recent upsurge of interest in the ways that thought may shape and be shaped by action, gesture, cultural experience, and language sets the stage for, but so far has not fully accomplished, the inclusion of Anthropology as an equal partner. (shrink)

To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate tradeoffs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. (...) While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps. (shrink)

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)