Human cognition is extended and enacted. Drawing the boundaries of cognition to include the resources and attributes of the body and materiality allows an examination of how these components interact with the brain as a system, especially over cultural and evolutionary spans of time. Literacy and numeracy provide examples of multigenerational, incremental change in both psychological functioning and material forms. Though we think materiality, its central role in human cognition is often unappreciated, for reasons that include conceptual distribution over multiple (...) material forms, the unconscious transparency of cognitive activity in general, and the different temporalities of metaplastic change in neurons and cultural forms. (shrink)

Drawing on the material culture of the Ancient Near East as interpreted through Material Engagement Theory, the journey of how material number becomes a conceptual number is traced to address questions of how a particular material form might generate a concept and how concepts might ultimately encompass multiple material forms so that they include but are irreducible to all of them together. Material forms incorporated into the cognitive system affect the content and structure of concepts through their agency and affordances, (...) the capabilities and constraints they provide as the material component of the extended, enactive mind. Material forms give concepts the tangibility that enables them to be literally grasped and manipulated. As they are distributed over multiple material forms, concepts effectively become independent of any of them, yielding the abstract irreducibility that makes a concept like number what it is. Finally, social aspects of material use—collaboration, ordinariness, and time—have important effects on the generation and distribution of concepts. (shrink)

I respond to P. McLaughlin and O. Schlaudt’s critique of my analysis of the cross-cultural origins of numbers, noting that my work draws extensively upon number systems as ethnographically attested around the globe, and thus is based only in part on the important Mesopotamian case study. I place the work of Peter Damerow in its historical context, noting its genesis in Piaget’s genetic epistemology and the problems associated with applying Piaget’s developmental theory to societies. While Piaget assumed numeracy involves invariant (...) mental transformations, ongoing research in numerical cognition has been largely unsuccessful in identifying specific brain-bound mechanisms for numerical structure. Accordingly, I suggest the extended mind paradigm from the philosophy of mind may be a more fruitful approach, and detail such an approach using Material Engagement Theory. (shrink)

Two approaches to prehistoric numeracy are analyzed and compared. The first uses traditional archaeological methods and criteria to examine and characterize marks on prehistoric artifacts for the purpose of assessing whether they were notations. The second uses a theoretical framework in which cognition is extended—meaning that material forms are a component of the mind—in order to understand the role of counting devices in numerical cognition. Each answers a different question: The traditional approach is concerned with understanding the intent and meaning (...) of artifactual marks, while the extended approach focuses on how material forms contribute to numerical realization, explication, and elaboration. Both highlight ongoing issues in investigating prehistoric numeracy, which might benefit from a combined and expanded methodology. (shrink)

Using a model of cognition as extended and enactive, we examine the role of materiality in making minds as exemplified by lithics and writing, forms associated with conceptual thought and meta-awareness of conceptual domains. We address ways in which brain functions may change in response to interactions with material forms, the attributes of material forms that may cause such change, and the spans of time required for neurofunctional reorganization. We also offer three hypotheses for investigating co-influence and change in cognition (...) and material culture. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793. (shrink)

Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of (...) whether devices are used in counting, which ones are used, and how they are used. (shrink)

Creativity is often conceived in terms of insight, innovation, and invention realized through technical mastery and skill. Challenging this individualistic model are “inventions” like writing, something that surely gave no clue to the form it would ultimately take—script—or the ways in which it would reorganize behaviors and brains in the cognitive state known as literacy. Here writing is analyzed as a tool used collectively and collaboratively. Collective, collaborative use enabled the tool to become increasingly effective at eliciting specific behavioral and (...) psychological responses. Collective, collaborative use also subjected the tool to the combined force of the individual variability represented by different user and material combinations over time. Combined variability influenced tool form toward features reflecting both the average behavioral, physiological, and psychological capacities of the tool-using community and points of maximal usability. The result offers a new model of creativity, one based not on the individual but on collective, collaborative use and incremental change in behaviors and brains, materially accumulated and redistributed between generations. The model presents aspects of human innovation that escape the individualistic model by focusing on ordinary tool-using behaviors and sustained use within social groups as the critical elements. (shrink)

The visuospatial system integrates inner and outer functional processes, organizing spatial, temporal, and social interactions between the brain, body, and environment. These processes involve sensorimotor networks like the eye–hand circuit, which is especially important to primates, given their reliance on vision and touch as primary sensory modalities and the use of the hands in social and environmental interactions. At the same time, visuospatial cognition is intimately connected with memory, self-awareness, and simulation capacity. In the present article, we review issues associated (...) with investigating visuospatial integration in extinct human groups through the use of anatomical and behavioral data gleaned from the paleontological and archaeological records. In modern humans, paleoneurological analyses have demonstrated noticeable and unique morphological changes in the parietal cortex, a region crucial to visuospatial management. Archaeological data provides information on hand–tool interaction, the spatial behavior of past populations, and their interaction with the environment. Visuospatial integration may represent a critical bridge between extended cognition, self-awareness, and social perception. As such, visuospatial functions are relevant to the hypothesis that human evolution is characterized by changes in brain–body–environment interactions and relations, which enhance integration between internal and external cognitive components through neural plasticity and the development of a specialized embodiment capacity. We therefore advocate the investigation of visuospatial functions in past populations through the paleoneurological study of anatomical elements and archaeological analysis of visuospatial behaviors. (shrink)

Introduction to the special issue in Pragmatics & Cognition focused on creativity, cognition, and material culture. With contributions from Maurice Bloch, Chris Gosden, Tim Ingold, John Kirsh, Carl Knappett & Sander van der Leeuw, Lambros Malafouris, Frédéric Vallée-Tourangeau, Kevin Warwick, and Tom Wynn and Frederick L. Coolidge.

This inquiry seeks to understand how the original form of writing in Mesopotamia—the small pictures and conventions of protocuneiform—became cuneiform, a script that could not be read without acquiring the neurological and behavioral reorganizations understood today as literacy. The process is described as involving small neurological and behavioral changes realized, accumulated, and distributed to new users through interactions with and concomitant incremental changes in the material form of writing. A related inquiry focuses on why and how numerical notations differ from (...) other written signs. Crucially, numerical signs instantiate their meaning, a representational mode that contrasts with the signification used to represent non-numerical language and which makes numerical notations contiguous with their unwritten precursors, technologies like fingers, tallies, and counters. Instantiation is related to the perceptual system for quantity; this so-called number sense influences the function and form of numerical signs. Reading is then discussed as a cognitive activity that necessarily involves a material form, a plausible example of extended cognition. Because numerical notations share function and often form with precursor technologies, if the former participate in extended cognition, the latter likely do as well. In conjunction with the contiguity between numerical notations and their unwritten precursors, this complicates the idea that (all) writing is (just) language. Finally, potential follow-on research is suggested. (shrink)

Humans leverage material forms for unique cognitive purposes: We recruit and incorporate them into our cognitive system, exploit them to accumulate and distribute cognitive effort, and use them to recreate phenotypic change in new individuals and generations. These purposes are exemplified by writing, a relatively recent tool that has become highly adept at eliciting specific psychological and behavioral responses in its users, capability it achieved by changing in ways that facilitated, accumulated, and distributed incremental behavioral and psychological change between individuals (...) and generations. Writing is described here as a self-organizing system whose design features reflect points of maximal usefulness that emerged under sustained collective use of the tool. Such self-organization may hold insights applicable to human cognitive evolution and tool use more generally. Accordingly, this article examines the emergence of the ability to leverage material forms for cognitive purposes, using the tool-using behaviors and lithic technologies of ancestral species and contemporary non-human primates as proxies for matters like collective use, generational sustainment, and the non-teleological emergence of design features. (shrink)

Complex systems like literacy and numeracy emerge through multigenerational interactions of brains, behaviors, and material forms. In such systems, material forms – writing for language and notations for numbers – become increasingly refined to elicit specific behavioral and psychological responses in newly indoctrinated individuals. These material forms, however, differ fundamentally in things like semiotic function: language signifies, while numbers instantiate. This makes writing for language able to represent the meanings and sounds of particular languages, while notations for numbers are semantically (...) meaningful without phonetic specification. This representational distinction is associated with neurofunctional and behavioral differences in what neural activity and behaviors like handwriting contribute to literacy and numeracy. In turn, neurofunctional and behavioral differences place written representations for language and numbers under different pressures that influence the forms they take and how those forms change over time as they are transmitted across languages and cultures. (shrink)

In their recent paper on “Challenges in mathematical cognition”, Alcock and colleagues (Alcock et al. [2016]. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41) defined a research agenda through 26 specific research questions. An important dimension of mathematical cognition almost completely absent from their discussion is the cultural constitution of mathematical cognition. Spanning work from a broad range of disciplines – including anthropology, archaeology, cognitive science, history of science, linguistics, philosophy, and psychology – we (...) argue that for any research agenda on mathematical cognition the cultural dimension is indispensable, and we propose a set of exemplary research questions related to it. (shrink)

Carey leaves unaddressed an important evolutionary puzzle: In the absence of a numeral list, how could a concept of natural number ever have arisen in the first place? Here we suggest that the initial development of natural number must have bootstrapped on a material culture scaffold of some sort, and illustrate how this might have occurred using strings of beads.

This is a book about numbers– what they are as concepts and how and why they originate–as viewed through the material devices used to represent and manipulate them. Fingers, tallies, tokens, and written notations, invented in both ancestral and contemporary societies, explain what numbers are, why they are the way they are, and how we get them. Cognitive archaeologist Karenleigh A. Overmann is the first to explore how material devices contribute to numerical thinking, initially by helping us to visualize and (...) manipulate the perceptual experience of quantity that we share with other species. She explores how and why numbers are conceptualized and then elaborated, as well as the central role that material objects play in both processes. Overmann’s volume thus offers a view of numerical cognition that is based on an alternative set of assumptions about numbers, their material component, and the nature of the human mind and thinking. Karim Zahidi (“Radicalizing numerical cognition,” Synthese, 2021, p. 530) called this reconstruction, as presented in journal articles, a “naturalistically plausible account of the emergence of the modern natural number concept," while César Dos Santos ("Review of: 'The Materiality of Numbers'," Qeios, 2023, p. 1) called it "a 'Copernican Revolution' in the way we understand the relationship between numbers and the material devices we use to record and manipulate them." . (shrink)

In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. Similarities between (...) the two number systems were then used to argue that archaic Mesopotamian numbers, like those of Polynesia, were highly elaborated and would have served as cognitively efficient tools for mental calculation. Their differences also show the importance of material technologies like tokens, impressions, and notations to developing mathematics. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793. (shrink)

What are numbers, and where do they come from? A novel answer to these timeless questions is proposed by cognitive archaeologist Karenleigh A. Overmann, based on her groundbreaking study of material devices used for counting in the Ancient Near East—fingers, tallies, tokens, and numerical notations—as interpreted through the latest neuropsychological insights into human numeracy and literacy. The result, a unique synthesis of interdisciplinary data, outlines how number concepts would have been realized in a pristine original condition to develop into one (...) of the ancient world’s greatest mathematical traditions, a foundation for mathematical thinking today. In this view, numbers are abstract from their inception and materially bound at their most elaborated. The research updates historical work on Neolithic tokens and interpretations of Mesopotamian numbers, challenging several longstanding assumptions about numbers in the process. The insights generated are also applied to the role of materiality in human cognition more generally, including how concepts become distributed across and independent of the material forms used for their representation and manipulation; how societies comprised of average individuals use material structures to create elaborated systems of numeracy and literacy; and the differences between thinking through and thinking about materiality. (shrink)

The idea the New Zealand Māori once counted by elevens has been viewed as a cultural misunderstanding originating with a mid-nineteenth-century dictionary of their language. Yet this “remarkable singularity” had an earlier, Continental origin, the details of which have been lost over a century of transmission in the literature. The affair is traced to a pair of scientific explorers, René-Primevère Lesson and Jules Poret de Blosseville, as reconstructed through their publications on the 1822–1825 circumnavigational voyage of the Coquille, a French (...) corvette. Possible explanations for the affair are briefly examined, including whether it might have been a prank by the Polynesians or a misunderstanding or hoax on the part of the Europeans. Reasons why the idea of counting by elevens remains topical are discussed. First, its very oddity has obscured the counting method actually used—setting aside every tenth item as a tally. This “ephemeral abacus” is examined for its physical and mental efficiencies and its potential to explain aspects of numerical structure and vocabulary (e.g., Mangarevan binary counting; the Hawaiian number word for twenty, iwakalua), matters suggesting material forms have a critical if underappreciated role in realising concepts like exponential value. Second, it provides insight into why it can be difficult to appreciate highly elaborated but unwritten numbers like those found throughout Polynesia. Finally, the affair illuminates the difficulty of categorising number systems that use multiple units as the basis of enumeration, like Polynesian pair-counting; potential solutions are offered. (shrink)

This essay introduces a special issue focused on 4E cognition (cognition as embodied, embedded, enactive, and extended) in the Lower Palaeolithic. In it, we review the typological and representational cognitive approaches that have dominated the past fifty years of paleoanthropology. These have assumed that all representations and computations take place only inside the head, which implies that the archaeological record can only be an “external” product or the behavioral trace of “internal” representational and computational processes. In comparison, the 4E approach (...) helps us to overcome this dualist representational logic, allowing us to engage directly with the archaeological record as an integral part of the thinking process, and thus ground a more parsimonious cognitive archaeology. It also treats stone tools, the primary vestiges of hominin thinking, as active participants in mental life. The 4E approach offers a better grounding for understanding hominin technical expertise, a crucially important component of hominin cognitive evolution. (shrink)

Cognitive archaeology is a relatively new interdisciplinary science that uses cognitive and psychological models to explain archaeological artifacts like stone tools, figurines, and art. Edited by cognitive archaeologist Karenleigh A. Overmann and psychologist Frederick L. Coolidge, Squeezing Minds From Stones is a collection of essays, from both early pioneers and 'up and coming' newcomers in the field, that addresses a wide variety of cognitive archaeology topics, including the value of experimental archaeology, primate archaeology, the intent of ancient tool makers, and (...) how they may have lived and thought. (shrink)

Four perspectives on numerical origins are examined. The nativist model sees numbers as an aspect of numerosity, the biologically endowed ability to appreciate quantity that humans share with other species. The linguistic model sees numbers as a function of language. The embodied model sees numbers as conceptual metaphors informed by physical experience and expressed in language. Finally, the extended model sees numbers as conceptual outcomes of a cognitive system that includes material forms as constitutive components. If numerical origins are to (...) be found, each perspective must address one or more critical questions that will require working across discipline boundaries. (shrink)

A review of Geoffrey B. Saxe, Cultural Development of Mathematical Ideas. Saxe offers a comprehensive treatment of social and linguistic change in the number systems used for economic exchange in the Oksapmin community of Papua New Guinea. By taking the cognition-is-social approach, Saxe positions himself within emerging perspectives that view cognition as enacted, situated, and extended. The approach is somewhat risky in that sociality surely does not exhaust cognition. Brains, bodies, and materiality also contribute to cognition—causally at least, and possibly (...) constitutively as well (as argued by Clark & Chalmers; Renfrew & Malafouris). This omission necessarily excludes the material dimension of numeracy. (shrink)