The material origin of numbers: Insights from the archaeology of the Ancient Near East

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

The material difference in human cognition

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

Squeezing minds from stones: Cognitive archaeology and the evolution of the human mind

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

Common creativity

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

A new look at old numbers, and what it reveals about numeration

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

The curious idea that Māori once counted by elevens, and the insights it still holds for cross-cultural numerical research

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

A cognitive archaeology of writing: Concepts, models, goals

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

4E cognition in the Lower Palaeolithic: An introduction

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

Early writing: A cognitive archaeological perspective on literacy and numeracy

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

Materiality in numerical cognition

Using the Material Engagement Theory of Cognitive Archaeologist Lambros Malafouris as its framework, the thesis offers a unique synthesis of data from neuroscience, ethnography, linguistics, and archaeology to outline how number concepts are realized, manipulated, and elaborated. The process is described as an interactivity of psychological processes like numerosity, behaviors that manipulate objects into concept-generating stimuli, and material objects with semiotic qualities distinct from those of language and agency distinct from that of brains and bodies. The counting technologies of the Ancient Near East (ANE) are then analyzed through archaeological and textual evidence spanning the late Upper Paleolithic to the Bronze Age, from the first realization of number concepts in a pristine original condition to their elaboration into one of the ancient world’s greatest mathematical traditions, a foundation for mathematical thinking today. Insights from the way numbers are realized through psychological–behavioral–material interactivity are used to challenge three dominant conceptualizations of ANE numbers: first, the idea that the ANE numerical lexicon would have counted only to very low numbers; second, that Neolithic tokens were the first counting technology; and third, that numbers were ‘concrete’ before they became ‘abstract’. Considering archaeological evidence from the Epipaleolithic Levant and drawing on linguistic and ethnographic evidence to characterize the regional prehistory, the thesis suggests that the numerical lexicon would have included relatively high numbers prior to the Neolithic; that finger-counting (linguistically attested) and tallies (archaeologically attested) would have preceded tokens; and that numbers are ‘abstract’ concepts whose content changes in conjunction with the incorporation and use of different material forms. The evidence provided to support these alternatives implies that numbers may have originated in the late Upper Paleolithic and arithmetic early in the Neolithic, pushing the onset of these capabilities further back than is commonly held. In addition to tallies and tokens, the thesis explores fingers and numerical notations as material artifacts, enabling an analysis of how materiality might structure numerical concepts, influence a number system’s capabilities, limitations, and elaboration potential, and affect brains and behavior over cultural spans of time. Insights generated by the case study are then applied to the role of materiality in cognition more generally, including how concepts become distributed across multiple material forms; the reasons why materiality might be transparent (or invisible) in cognition; and the differences between thinking through and thinking about materiality.</p