Book review: Reckonings: Numerals, cognition, and history (original) (raw)

From number sense to number symbols. An archaeological perspective

Philosophical Transactions of the Royal Society B, 2017

How and when did hominins move from the numerical cognition that we share with the rest of the animal world to number symbols? Objects with sequential markings have been used to store and retrieve numerical information since the beginning of the European Upper Palaeolithic (42 ka). An increase in the number of markings and complexity of coding is observed towards the end of this period. The application of new analytical techniques to a 44–42 ka old notched baboon fibula from Border Cave, South Africa, shows that notches were added to this bone at different times, suggesting that devices to store numerical information were in use before the Upper Palaeolithic. Analysis of a set of incisions on a 72–60 ka old hyena femur from the Les Pradelles Mousterian site, France, indicates, by comparison with markings produced by modern subjects under similar constraints, that the incisions on the Les Pradelles bone may have been produced to record, in a single session, homologous units of numeri...

Enculturation and the historical origins of number words and concepts

Synthese, 2021

In the literature on enculturation--the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture--numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical.

Six Unresolved Questions in the Early History of Numeration

Signs of Writing: The Cultural, Social, and Linguistic Contexts of the World’s First Writing Systems, 2014

Across multiple disciplines, written numerical notation is a topic of keen interest, yet several unresolved issues in its analysis are either elided or taken as settled. Numerical notation is a complex phenomenon with multiple independent histories—more than 100 distinct systems used over the past 5,500 years, interweaving with, rather than strictly paralleling, the histories of writing systems. Social, semiotic, and cognitive approaches are brought to bear on six incompletely answered questions about numeration in relation to the earliest writing. Is numerical notation a necessary precursor to writing? Does the earliest numerical notation initially serve a bookkeeping function for early states? What is the relationship between tallying and numerical notation? Does the use of numerical notation change human cognition about the domain of number? How does the emergence of numerical notation relate to linguistic representations of number? Finally, among all domains of knowledge, why is number so widely represented using graphic notations? Recognizing that these issues are not resolved, and identifying different possible resolutions, must be preliminary to fully integrating numerical notation within the broader history of writing.

The materiality of numbers: Emergence and elaboration from prehistory to present

Cambridge University Press, 2023

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.

Re-evaluating merit: Multiple overlapping factors explain the evolution of numerical notations

How should we evaluate the merit of written numeral systems? The present ubiquity of the Hindu-Arabic (Western) numerals might suggest that narrow considerations of efficiency have promoted the convergence of numerical traditions on a single, superior solution. Comparing the historical evolution of numerical notations to the history of writing systems suggests, instead, that a host of social factors influence the adoption, transmission, retention and replacement of numeral systems. The wide range of contextual uses and functions of written numerals belie any simple explanation of the choices underlying their abandonment. Following the criteria outlined by Coulmas, a sociolinguistic model is proposed in which a wide variety of technical, graphic and cultural factors must be considered in order to fully explain the historical record.