The limits of counting: numerical cognition between evolution and culture

Body-based units of measure in cultural evolution

Measurement systems are important drivers of cultural and technological evolution. However, the evolution of measurement is still insufficiently understood. Many early standardized measurement systems evolved from body-based units of measure, such as the cubit and fathom, but researchers have rarely studied how or why body-based measurement has been used. We documented body-based units of measure in 186 cultures, illustrating how body-based measurement is an activity common to cultures around the world. Here, we describe the cultural and technological domains these units are used in. We argue that body-based units have had, and may still have, advantages over standardized systems, such as in the design of ergonomic technologies. This helps explain the persistence of body-based measurement centuries after the first standardized measurement systems emerged.

Pedagogical Ecology for an Alternative Sustainability: With Insights from Francis of Assisi and Contemporary Life Sciences

Sustainability is a widely discussed issue nowadays. The “human factor” appears to be the key to a suitable theory of sustainable development and, even more, to understanding the real scope of the issue at stake. We begin by highlighting that the issue of sustainability and the related ecological crisis ultimately stem from the fundamental view of the human–environment relationships. We tackle such a fundamental view from two apparently distant but converging perspectives: the one of Francis of Assisi (the patron saint of ecologists) and the one of contemporary advancements in evolutionary biology known as the “extended evolutionary theory” (EES). This will allow us to highlight how current life sciences ground a strong form of organism–environment complementarity—a core point for any allegedly comprehensive approach to sustainability and ecology. After that, we focus on recent developments in cultural evolution studies that see culture both as the driving force of (recent) human evolution and as the general context where the human–environment relationships take place and develop. Therefore, we argue that the environment exerts a powerful pedagogical influence on the human being and on humanity as a whole. We conclude by proposing a pedagogical criterion for ecology and sustainable development, according to which the modifications caused by the human being to the environment must be assessed (also) for their pedagogical import.

The perception of quantity ain't number: Missing the primacy of symbolic reference

Clarke and Beck's defense of the theoretical construct "approximate number system" (ANS) is flawed in serious ways - from biological misconceptions to mathematical naïveté. The authors misunderstand behavioral/psychological technical concepts, such as numerosity and quantical cognition, which they disdain as "exotic." Additionally, their characterization of rational numbers is blind to the essential role of symbolic reference in the emergence of number.

The history of number words in the world's languages-what have we learnt so far?

For over 100 years, researchers from various disciplines have been enthralled and occupied by the study of number words. This article discusses implications for the study of deep history and human evolution that arise from this body of work. Phylogenetic modelling shows that low-limit number words are preserved across thousands of years, a pattern consistently observed in several language families. Cross-linguistic frequencies of use and experimental studies also point to widespread homogeneity in the use of number words. Yet linguistic typology and field documentation reports caution against positing a privileged linguistic category for number words, showing a wealth of variation in how number words are encoded across the world. In contrast with low-limit numbers, the higher numbers are characterized by a rapid and morphologically consistent pattern of expansion, and behave like grammatical phrasal units, following language-internal rules. Taken together, the evidence suggests that numbers are at the cross-roads of language history. For languages that do have productive and consistent number systems, numerals one to five are among the most reliable available linguistic fossils of deep history, defying change yet still bearing the marks of the past, while higher numbers emerge as innovative tools looking to the future, derived using language-internal patterns and created to meet the needs of modern speakers. This article is part of the theme issue 'Reconstructing prehistoric languages'.

Numeral Systems Across Languages Support Efficient Communication: From Approximate Numerosity to Recursion

Languages differ qualitatively in their numeral systems. At one extreme, some languages have a small set of number terms, which denote approximate or inexact numerosities; at the other extreme, many languages have forms for exact numerosities over a very large range, through a recursively defined counting system. Why do numeral systems vary as they do? Here, we use computational analyses to explore the numeral systems of 30 languages that span this spectrum. We find that these numeral systems all reflect a functional need for efficient communication, mirroring existing arguments in other semantic domains such as color, kinship, and space. Our findings suggest that cross-language variation in numeral systems may be understood in terms of a shared functional need to communicate precisely while using minimal cognitive resources.

Is thirty-two three tens and two ones? The embedded structure of cardinal numbers

The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make 'infinite use of finite means' (or that numbers are generative) has been left unanswered. While previous theories rely on the idea of the successor principle, we propose an alternative hypothesis that children's understanding of the syntactic rules for building complex numerals-or numerical syntax-is a crucial foundation for the acquisition of number concepts. In two independent studies, we assessed children's understanding of numerical syntax by probing their knowledge about the embedded structure of cardinal numbers using a novel task called Give-a-number Base-10 (Give-N10). In Give-N10, children were asked to give a large number of items (e.g., 32 items) from a pool that is organized in sets of ten items. Children's knowledge about the embedded structure of numbers (e.g., knowing that thirty-two items are composed of three tens and two ones) was assessed from their ability to use those sets. Study 1 tested English-speaking 4- to 10-year-olds and revealed that children's understanding of the embedded structure of numbers emerges relatively late in development (several months into kindergarten), beyond when they are capable of making a semantic induction over a local sequence of numbers. Moreover, performance in Give-N10 was predicted by other task measures that assessed children's knowledge about the syntactic rules that govern numerals (such as counting fluency), demonstrating the validity of the measure. In Study 2, this association was tested again in monolingual Korean kindergarteners (5-6 years), as we aimed to test the same effect in a language with a highly regular numeral system. It replicated the association between Give-N10 performance and counting fluency, and it also demonstrated that Korean-speaking children understand the embedded structure of cardinal numbers earlier in the acquisition path than English-speaking peers, suggesting that regularity in numerical syntax facilitates the acquisition of generative properties of numbers. Based on these observations and our theoretical analysis of the literature, we propose that the syntax for building complex numerals, not the successor principle, represents a structural platform for numerical thinking in young children.

Editors' Review and Introduction: The Cultural Evolution of Cognition

This topic addresses a question of key interest to cognitive science, namely which factors may have triggered, constrained, or shaped the course of cognitive evolution. It highlights the relevance of culture as a driving force in this process, with a special focus on social learning and language, conceptual tools, and material culture. In so doing, the topic combines two goals: to provide an overview of current empirical and theoretical work leading this field, tailored for a wider cognitive science audience, and to investigate the potential for integrating multiple perspectives across several timescales and levels of analysis, from the microlevel of individual behavior to the macrolevel of cultural change and language diversification. One key purpose is to assess the extent to which the different research approaches can cross-fertilize each other, thereby also contributing to the advancement of cognitive science more broadly.

What Early Sapiens Cognition Can Teach Us: Untangling Cultural Influences on Human Cognition Across Time

Evidence of cultural influences on cognition is accumulating, but untangling these cultural influences from one another or from non-cultural influences has remained a challenging task. As between-group differences are neither a sufficient nor a necessary indicator of cultural impact, cross-cultural comparisons in isolation are unable to furnish any cogent conclusions. This shortfall can be compensated by taking a diachronic perspective that focuses on the role of culture for the emergence and evolution of our cognitive abilities. Three strategies for reconstructing early human cognition are presented: the chaîne opératoire approach and its extension to brain-imaging studies, large-scale extrapolations, and phylogenetic comparative methods. While these strategies are reliant on our understanding of present-day cognition, they conversely also have the potential to advance this understanding in fundamental ways.

Is There Really an Evolved Capacity for Number?

Humans and other species have biologically endowed abilities for discriminating quantities. A widely accepted view sees such abilities as an evolved capacity specific for number and arithmetic. This view, however, is based on an implicit teleological rationale, builds on inaccurate conceptions of biological evolution, downplays human data from non-industrialized cultures, overinterprets results from trained animals, and is enabled by loose terminology that facilitates teleological argumentation. A distinction between quantical (e.g., quantity discrimination) and numerical (exact, symbolic) cognition is needed: quantical cognition provides biologically evolved preconditions for numerical cognition but it does not scale up to number and arithmetic, which require cultural mediation. The argument has implications for debates about the origins of other special capacities - geometry, music, art, and language.

A Multidisciplinary Approach to Research in Small-Scale Societies: Studying Emotions and Facial Expressions in the Field

Although cognitive science was multidisciplinary from the start, an under-emphasis on anthropology has left the field with limited research in small scale, indigenous societies. Neglecting the anthropological perspective is risky, given that once-canonical cognitive science findings have often been shown to be artifacts of enculturation rather than cognitive universals. This imbalance has become more problematic as the increased use of Western theory-driven approaches, many of which assume human uniformity ("universality"), confronts the absence of a robust descriptive base that might provide clarifying or even contrary evidence. We highlight the need for remedies to such shortcomings by suggesting a two-fold methodological shift. First, studies conducted in indigenous societies can benefit by relying on multidisciplinary research groups to diminish ethnocentrism and enhance the quality of the data. Second, studies devised for Western societies can readily be adapted to the changing settings encountered in the field. Here, we provide examples, drawn from the areas of emotion and facial expressions, to illustrate potential solutions to recurrent problems in enhancing the quality of data collection, hypothesis testing, and the interpretation of results.

Current Perspectives on Cognitive Diversity

To what extent is cognition influenced by a person’s cultural background? This question has remained controversial in large fields of the cognitive sciences, including cognitive psychology, and is also underexplored in anthropology. In this perspective article, findings from a recent wave of cross-cultural studies will be outlined with respect to three aspects of cognition: perception and categorization, number representation and counting, and explanatory frameworks and beliefs. Identifying similarities and differences between these domains allows for general conclusions regarding cognitive diversity and helps to highlight the importance of culturally shaped content for a comprehensive understanding of cognition.

Counting or chunking? Mathematical and heuristic abilities in patients with corticobasal syndrome and posterior cortical atrophy

A growing amount of empirical data is showing that the ability to manipulate quantities in a precise and efficient fashion is rooted in cognitive mechanisms devoted to specific aspects of numbers processing. The analog number system (ANS) has a reasonable representation of quantities up to about 4, and represents larger quantities on the basis of a numerical ratio between quantities. In order to represent the precise cardinality of a number, the ANS may be supported by external algorithms such as language, leading to a "precise number system". In the setting of limited language, other number-related systems can appear. For example the parallel individuation system (PIS) supports a "chunking mechanism" that clusters units of larger numerosities into smaller subsets. In the present study we investigated number processing in non-aphasic patients with corticobasal syndrome (CBS) and posterior cortical atrophy (PCA), two neurodegenerative conditions that are associated with progressive parietal atrophy. The present study investigated these number systems in CBS and PCA by assessing the property of the ANS associated with smaller and larger numerosities, and the chunking property of the PIS. The results revealed that CBS/PCA patients are impaired in simple calculations (e.g., addition and subtraction) and that their performance strongly correlates with the size of the numbers involved in these calculations, revealing a clear magnitude effect. This magnitude effect was correlated with gray matter atrophy in parietal regions. Moreover, a numeral-dots transcoding task showed that CBS/PCA patients were able to take advantage of clustering in the spatial distribution of the dots of the array. The relative advantage associated with chunking compared to a random spatial distribution correlated with both parietal and prefrontal regions. These results shed light on the properties of systems for representing number knowledge in non-aphasic patients with CBS and PCA.

Mangarevan invention of binary steps for easier calculation

When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition.

How thought is mapped into words

To English speakers, the distinctions between blue and green, cup and glass, or cut and break seem self-evident. The intuition is that these words label categories that have an existence independent of language, and language merely captures the pre-existing categories. But cross-linguistic work shows that the named distinctions are not nearly as self-evident as they may feel. There is diversity in how languages divide up domains including color, number, plants and animals, drinking vessels and household containers, body parts, spatial relations, locomotion, acts of cutting and breaking, acts of carrying and holding, and more. Still, studies documenting variability across languages also uncover striking commonalities. Such commonalities indicate that there are sources of constraint on the variation. Both the commonalities and divergences carry important lessons for Cognitive Science. They speak to the causal relations among language, thought, and culture; the possibility of cross-culturally shared aspects of perception and cognition; the methods needed for studying general-purpose, nonlinguistic concepts; and how languages are learned. WIREs Cogn Sci 2013, 4:583-597. doi: 10.1002/wcs.1251 CONFLICT OF INTEREST: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

Cognition is … Fundamentally Cultural

A prevailing concept of cognition in psychology is inspired by the computer metaphor. Its focus on mental states that are generated and altered by information input, processing, storage and transmission invites a disregard for the cultural dimension of cognition, based on three (implicit) assumptions: cognition is internal, processing can be distinguished from content, and processing is independent of cultural background. Arguing against each of these assumptions, we point out how culture may affect cognitive processes in various ways, drawing on instances from numerical cognition, ethnobiological reasoning, and theory of mind. Given the pervasive cultural modulation of cognition—on all of Marr’s levels of description—we conclude that cognition is indeed fundamentally cultural, and that consideration of its cultural dimension is essential for a comprehensive understanding.

Nature and culture of finger counting: diversity and representational effects of an embodied cognitive tool

Studies like the one conducted by Domahs et al. (2010, in Cognition) corroborate that finger counting habits affect how numbers are processed, and legitimize the assumption that this effect is culturally modulated. The degree of cultural diversity in finger counting, however, has been grossly underestimated in the field at large, which, in turn, has restricted research questions and designs. In this paper, we demonstrate that fingers as a tool for counting are not only naturally available, but are also-and crucially so-culturally encoded. To substantiate this, we outline the variability in finger counting and illustrate each of its types with instances from the literature. We argue that the different types of finger counting all constitute distinct representational systems, and we use their properties-dimensionality, dimensional representation, base and sub-base values, extendibility and extent, sign count, and regularity-to devise a typology of such systems. This allows us to explore representational effects, that is, the cognitive implications these properties may have, for instance, for the efficiency of information encoding and representation, ease of learning and mastering the system, or memory retrieval and cognitive load. We then highlight the ambivalent consequences arising from structural inconsistencies between finger counting and other modes of number representation like verbal or notational systems, and we discuss how this informs questions on the evolution and development of counting systems. Based on these analyses, we suggest some directions for future research in the field of embodied cognition that would profit substantially from taking into account the cultural diversity in finger counting.

Causal asymmetry across cultures: assigning causal roles in symmetric physical settings

Causal cognition in the physical domain has been treated for a long time as if it were (1) objective and (2) independent of culture. Despite some evidence to the contrary, however, these implicit assumptions have been rarely ever explored systematically. While the pervasive tendency of people to consider one of two equally important entities as more important for bringing about an effect (as reported by White, 2006) meanwhile provides one type of counter-evidence for the first assumption, respective findings remained mute to the second. In order to scrutinize how robust such tendencies are across cultures - and, if not, on which aspects of culture they may depend - we asked German and Tongan participants to assign prime causality in nine symmetric settings. For most settings, strong asymmetries in both cultures were found, but not always in the same direction, depending on the task content and by virtue of the multifaceted character of "culture." This indicates that causal asymmetries, while indeed being a robust phenomenon across cultures, are also modulated by task-specific properties (such as figure-ground relations), and are subject to cultural influences.

Cultural Variation in Numeration Systems and Their Mapping Onto the Mental Number Line

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, this article argues for the inclusion of cross-linguistic analyses. It scrutinizes 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.

The cultural constitution of cognition: taking the anthropological perspective

To what extent is cognition affected by culture? And how might cognitive science profit from an intensified collaboration with anthropology in exploring this issue? In order to answer these questions, we will first give a brief description of different perspectives on cognition, one that prevails in most cognitive sciences – particularly in cognitive psychology – and one in anthropology. Three basic assumptions of cognitive science regarding the separability of content and process, the context-independence of processing, and the culture-independence of processing will then be discussed. We argue that these assumptions need to be questioned and scrutinized cross-culturally. A thorough examination of these issues would profit considerably from collaboration with anthropologists, not only by enabling deeper insight into the cultures under scrutiny, but also by synergistic effects that would allow for a more comprehensive understanding of human cognition.

Anthropology in cognitive science

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.

Forest chimpanzees (Pan troglodytes verus) remember the location of numerous fruit trees

It is assumed that spatial memory contributes crucially to animal cognition since animals' habitats entail a large number of dispersed and unpredictable food sources. Spatial memory has been investigated under controlled conditions, with different species showing and different conditions leading to varying performance levels. However, the number of food sources investigated is very low compared to what exists under natural conditions, where food resources are so abundant that it is difficult to precisely identify what is available. By using a detailed botanical map containing over 12,499 trees known to be used by the Taï chimpanzees, we created virtual maps of all productive fruit trees to simulate potential strategies used by wild chimpanzees to reach resources without spatial memory. First, we simulated different assumptions concerning the chimpanzees' preference for a particular tree species, and, second, we varied the detection field to control for the possible use of smell to detect fruiting trees. For all these assumptions, we compared simulated distance travelled, frequencies of trees visited, and revisit rates with what we actually observed in wild chimpanzees. Our results show that chimpanzees visit rare tree species more frequently, travel shorter distances to reach them, and revisit the same trees more often than if they had no spatial memory. In addition, we demonstrate that chimpanzees travel longer distances to reach resources where they will eat for longer periods of time, and revisit resources more frequently where they ate for a long period of time during their first visit. Therefore, this study shows that forest chimpanzees possess a precise spatial memory which allows them to remember the location of numerous resources and use this information to select the most attractive resources.

Look Ma, no fingers! Are children numerical solipsists?

I ask whether it is necessary that principles of number be mentally represented and point to the role of language in determining cultural variation. Some cultures possess extensive counting systems that are finite. I suggest that learning number principles is similar to learning conservation and, as such, might be derived from learning about the empirical properties of objects and other individuals in combinations.