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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.
Figures
Tables
Acknowledgments
Foreword
Preface
Numbers in a Nutshell
What Numbers Are as Concepts
The Working Definition of Number
Analyzing Numbers through an Existing Familiarity
Who Has Numbers? And Do We All Have the Same Numbers?
Variability between Cultural Number Systems
Explaining Cross-Cultural Variability
Change within Any Particular Cultural Tradition
Are Numbers Ever the Same, and If So, How Are They the Same?
Converging Perspectives on Numbers
Historical Ideas about Where Numbers Come From
Four Recent Models of Numerical Origins
Historical Change in How We Study Number Systems
The Contributions and Challenges of Archaeology
The Brain in Numbers
Numerosity, the Innate Sense of Quantity
Categorization and Abstraction
The Mental Number Line
The Parietal Lobe and Numbers
The Cerebellum and Numbers
Finger-Counting and the Brain
Bodies and Behaviors
How Numbers Emerge and the Roles of the Fingers
How Using the Fingers Patterns Numerical Structure and Language
Finger-Counting in Proto-Languages
The Visual Experience of the Hand
Movement and Material Engagement
Counting Behaviors When Numbers Are Few
Language in Numbers
What Language Reveals about Numbers
Lexical Numbers, Finger-Counting, and Analyzability
Evidence for Numerosity in Ancient Languages
Numerical Organization and Structure
Necessary and Sufficient Conditions
Global and Regional Patterns
The Global Pattern: Numerical Emergence and Prehistoric Migration
The Regional Pattern: Numerical Elaboration and Socio- Material Complexity
Cultural Analogies
Materiality in Numbers
Recruiting New Devices as the Mechanism of Numerical Elaboration
Representing and Manipulating
Materially Anchored Conceptual Blending
General Effects of Material Culture
Materiality in Cognition
Cognition Is Extended and Enactive
Materiality Has Agency
Enactive Signification
Sustained Collaboration, Common Creativity
Making Quantity Tangible and Manipulable
Gaining Control of Quantity Percepts
The Instrumental Body
Using the Hand as a Material Device for Counting
The Hand’s Influence on Verbal Expressions
Finger-Counting Age
Tallies and Other Devices That Accumulate
Devices That Accumulate
Tallying and Numerical Organization and Structure
Taking Up the Material (Noncorporeal) Tally
Tokenization
Tallying without Words
Interpreting Prehistoric Artifacts
Mark-Making and Prehistoric Numbers
Archaeological Techniques for Interpreting Prehistoric Marks
A Cautionary Tale: The Australian Message Sticks
Interpreting Palaeolithic Artifacts as Possible Tallies
Functional Considerations
Devices That Accumulate and Group
The Inka Counting Board
Oceanian Counting by Sorting and the “Ephemeral Abacus”
The Yoruba Cowrie Abacus
Handwritten Notations
Contiguity of Function between Numerical Notations and Precursor Technologies
Differences between Written Numbers and Writing for Nonnumerical Language
What Writing – Numerical and Not – Adds to Numbers
Major Trends
The Materiality of Numbers
Future Directions in Research
A Final Thought
References
Index