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- Number concepts are constructed through material engagement: A reply to Sutliff, Read, and Everett
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The article replies to commentary on "Numerosity structures the expression of quantity in lexical numbers and grammatical number" (published by Current Anthropology in 2015).
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- Bootstrapping Ordinal Thinking
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Chapter 9 in T. Wynn & F.L. Coolidge (eds), Formal cognitive models in Paleolithic archeology.
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- Material scaffolds in numbers and time
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The paper interprets Upper Paleolithic artifacts using a framework of material complexity, numeration systems, and timekeeping based on cultural categorizations, insights on the emergence of number terms in language, and astronomy practices of 33 contemporary hunter–gatherer societies. Key findings: (1) an absence of societies with minimal material complexity and later-stage numeration systems, suggesting that material scaffolding may be important to realizing explicit number concepts, (2) the consistency of material complexity with both early- and later-stage numeration systems, emphasizing that material complexity may precede and inform the development of complexity in numeration systems, (3) the compatibility of astronomical practices with the spectrum of complexity in material culture and numeration systems, suggesting that the awareness of time may precede both, and (4) the increasing quantification of time consistent with greater material and numeration complexity, suggesting the availability of numbers as a cognitive technology may enable the structuring of time. These findings suggest that astronomy originates in the ability to estimate and infer contextual relations among natural phenomena and transitions from these natural associations to material representations and cognitive technologies that mediate conceptual apprehensions of time as a substance that can be quantified. As artifacts can scaffold explicit concepts of numbers and numbers explicit concepts of time, prehistoric artifacts may represent similar scaffolding and conceptual development. Prehistoric societies making these artifacts may have possessed, in addition to material complexity, abilities for expressing quantities in language and using material externalization and cognitive technologies. Further, the Abri Blanchard artifact may represent externalized working memory, a modern mind–material interaction.
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- On the nature of numerosity and the role of language in developing number concepts
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We respond to Caleb Everett’s (2013) critique of our 2012 Current Anthropology article “Numerosity, Abstraction, and the Emergence of Symbolic Thinking.” We refute Everett’s criticisms, including his claim that we overemphasized paleoanthropological evidence in our argument, noting that recent experimental research in numerical cognition comprised 60% of our references. We also identify two key misunderstandings by Everett, first, the idea that numerosity is not uniform in extant Homo sapiens (we believe that experimental findings, including those of Everett himself, demonstrate that quantity perception is cross-culturally uniform) and second, the idea that language necessarily shapes human numerosity (in fact, the two are largely independent cognitive processes, and the evidence shows that numerosity, as a perceptual primitive, precedes language, not the other way around as argued by Everett). We note our focus on the fundamental question of how discrete quantities emerge out of the undifferentiated ‘many’, given numerosity, and reiterate our 2012 suggestion that the answer lies in the interaction of quantity appreciation with material scaffolds.
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- Beyond writing: The development of literacy in the Ancient Near East
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Previous discussions of the origins of writing in the Ancient Near East have not incorporated the neuroscience of literacy, which suggests that when Mesopotamians wrote marks on clay in the late-fourth millennium, they inadvertently reorganized their neural activity, a factor in manipulating the writing system to reflect language, yielding literacy through a combination of neurofunctional change and increased script fidelity to language. Such a development appears to take place only with a sufficient demand for writing and reading, such as that posed by a state-level bureaucracy; the use of a material with suitable characteristics; and the production of marks that are conventionalized, handwritten, simple, and non-numerical. From the perspective of Material Engagement Theory, writing and reading represent the interactivity of bodies, materiality, and brains: movements of hands, arms, and eyes; clay and the implements used to mark it and form characters; and vision, motor planning, object recognition, and language. Literacy is a cognitive change that emerges from and depends upon the nexus of interactivity of the components.
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- The false dichotomy: A refutation of the Neandertal indistinguishability claim
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In the debate about the demise of the Neandertal, several scholars have claimed that humanity’s nearest relatives were indistinguishable archaeologically, and thus behaviorally and cognitively, from contemporaneous Homo sapiens. They suggest that to hold otherwise is to characterize Neandertals as inferior to H. sapiens, a false dichotomy that excludes the possibility that the two human types simply differed in ways visible to natural selection, including their cognition. Support of the Neandertal indistinguishability claim requires ignoring the cranial differences between the two human types, which have implications for cognition and behavior. Further, support of the claim requires minimizing asymmetries in the quantity and degree of behavioral differences as attested by the archaeological record. The present paper reviews the evidence for cognitive and archaeological differences between the two human types in support of the excluded middle position.
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- Numerosity, abstraction, and the emergence of symbolic thinking
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In this paper we tentatively propose that one of the feral cognitive bases for modern symbolic thinking may be numerosity, that is, the ability to appreciate and understand numbers. We proffer that numerosity appears to be an inherently abstractive process, which is supported by numerous human infant and monkey studies. We also review studies that demonstrate that the neurological substrate for numerosity is primarily the intraparietal sulcus of the parietal lobes, the angular and supramarginal gyri in the inferior parietal lobes, and areas of the prefrontal cortex. We also speculate that the lower level of abstraction involved in numerosity may serve as a basis for higher-level symbolic thinking, such as number and letter symbolism and sequencing. We further speculate that these two levels of abstraction may give rise to highly sophisticated characteristics of modern human language, such as analogizing and metaphorizing.
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- The role of materiality in numerical cognition
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Numerical elaboration and the extension of numbers to non-tangible domains such as time have been linked to cultural complexity in several studies. However, the reasons for this phenomenon remain insufficiently explored. In the present analysis, Material Engagement Theory, an emerging perspective in cognitive archaeology, provides a new perspective from which to reinterpret the cultural nexus in which quantification develops. These insights are then applied to representative Neolithic, Upper Palaeolithic, and Middle Stone Age artifacts used for quantification: clay tokens from Neolithic Mesopotamia, notched tallies from the European Upper Palaeolithic, hand stencils with possible finger-counting patterns as documented at Cosquer and Gargas, and stringed beads from Blombos Cave in South Africa.
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- Finger-counting in the Upper Palaeolithic
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Upper Palaeolithic hand stencils at Cosquer cave have been interpreted as forming a numeric code. The present analysis examined ‘digits’ at Cosquer and Gargas from the perspectives of modern ethnography, shared cognitive functioning and human hand anatomy, concluding that correspondences between the 27,000-year-old hand stencils and modern finger-counting practices, including the use of so-called biomechanically infeasible hand positions, are unlikely due to chance; thus, the hand stencils may indeed represent integers. Images of finger-signs may provide an additional avenue for interpreting Palaeolithic quantification.
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- Materiality and numerical cognition: A Material Engagement Theory perspective
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Chapter 5 in T. Wynn & F.L. Coolidge (eds), Formal cognitive models in Paleolithic archeology is a version of Chapter 2 of the thesis.
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- Creativity, cognition and material culture: An introduction
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A brief introduction to a special issue on "Creativity, cognition and material culture" in Pragmatics & Cognition.
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- Numbers and time: A cross-cultural investigation of the origin and use of numbers as a cognitive technology
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The study examined how numbers as a cognitive technology develops from material scaffolds and structures a cognitive domain such as time. Number concepts originate in numerosity and develop into explicit concepts through artifactual scaffolding that facilitates tactile and discrete representation. Once available, numbers structure time as a quantifiable substance, displacing methods of timekeeping based on estimating relations among natural environmental features. The method used was that of cross-cultural psychology. Behavioral data for 50 globally dispersed societies were compared to an index of material complexity. Variables of interest included highest number counted and timekeeping beliefs and behaviors. Significant correlations were found in five hypotheses relating increased cultural complexity to increased numeration system complexity and the increased use of quantification in timekeeping (small-to-medium effect sizes or greater). Three additional hypotheses were non-significant, demonstrating stability in finger-counting, social identity domains, and resourcing pragmatics, despite increased availability of numbers. While establishing causality was outside the scope, the results suggest the increased availability and use of numbers acts to structure conceptions of ‘time’ in quantified ways, measured through behaviors such as the increased use of material devices for counting time, the division of time into finer gradations, the counting of human age, the structuring of time into epochs, and the decreased use of height estimation techniques for timekeeping. However, the availability of numbers did not change the prevalence of finger-counting, astronomical myths, associating menstrual and lunar cycles, or using seasonal variation for timekeeping.
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- Numerosity structures the expression of quantity in lexical numbers and grammatical number
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Using data from the World Atlas of Language Structures and other sources, the present study analyzed 905 languages on grammatical number (GN) and lexical numbers (LN) to investigate what the distribution of these linguistic features might suggest about the relationship between language and numerosity, the perceptual system for quantity. Nearly 7% of the sample had LN but lacked GN, and GN never occurred without LN, implying that LN may develop first and that GN is neither necessary nor sufficient for developing LN, despite its role in helping children acquire number concepts when present as a feature of language. The geographic–temporal distribution of the two linguistic features additionally supported the idea that LN may emerge prior to GN. Further, the ‘one-two-three-many’ structure of both LN and GN, along with failure of historic AI modeling to converge on real-world number system solutions, suggested that numerosity may structure the expression of quantity in both linguistic domains. The role of the hand in numbers (the interaction of numerosity with cognitive processes such as finger gnosia, haptic perception, and neural reactions to tools) implies that LN may originate in tactile engagement with material structures that may subsequently extend to non-tactile domains such as GN.
