The numerical notation associated with texts and other representational media used in ancient societies is an important means by which past cognitive processes may be reconstructed. No satisfactory typology exists, however, to help understand the relationship between numerical symbols and cognitive processes. As a result, theories concerning the development of numeration remain mired in a unilinear and ethnocentric framework in which our own (Hindu-Arabic or Western) numerals are seen as the ultimate stage of evolution. It is suggested herein that there are two separate dimensions that need to be considered when classifying and evaluating numerical notation systems, and that these dimensions are structured in highly constrained ways. A new typology is presented in which systems are classified into five major types on the basis of these dimensions. Using this typology, a multilinear model is presented for the patterned diachronic change in numerical notation systems, which refutes both unilinear evolutionary theories and radically relativistic propositions regarding how individuals in pre-modern societies represented numbers.

This book is a cross-cultural reference volume of all attested numerical notation systems (graphic, non-phonetic systems for representing numbers), encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defies progressive, unilinear evolutionary models of change, Stephen Chrisomalis identifies five basic types of numerical notation systems, using a cultural phylogenetic framework to show relationships between systems and to create a general theory of change in numerical systems. Numerical notation systems are primarily representational systems, not computational technologies. Cognitive factors that help explain how numerical systems change relate to general principles, such as conciseness or avoidance of ambiguity, which apply also to writing systems. The transformation and replacement of numerical notation systems relates to specific social, economic, and technological changes, such as the development of the printing press or the expansion of the global world-system.

Success in academic archaeology is strongly influenced by the publication of peer-reviewed articles. Despite the importance of such articles, minimal research has explicitly examined the factors influencing publishing decisions in archaeology. In order to better understand the landscape of archaeological publishing, we distributed a short survey that solicited basic professional and demographic information before asking respondents to (1) identify journals that publish important archaeological research, (2) identify journals that people who read archaeological academic CVs value most highly, and (3) rank the factors that affected their decisions about where to submit an article for publication. Our results from 274 respondents generated a list of 167 individual journal titles. Prestige was viewed as the most important factor that affected publishing decisions, followed by audience and open access considerations. There was no relationship between respondent-generated journal rankings and SCImago Journal Ranks (SJR), but there were significant differences in average SJR by gender and career stage. Responses showed consensus on only a small number of highly ranked archaeology and science-subject journals, with little agreement on the importance of most other journals. We conclude by highlighting the areas of disciplinary consensus and divergence revealed by the survey and by discussing how implicit prestige hierarchies permeate academic archaeology.

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.

If cross-cultural researchers hope to contribute to cultural evolutionary theory, methods must be developed to describe and explain cultural processes. The distinction made by Boas between historical and comparative methods limited scholarly interest in the analysis of patterned historical change. Numerous techniques have been developed to draw diachronic inferences from synchronic ethnographic data, with varying degrees of success. The use of archaeological and historical data to draw diachronic inferences similarly has had mixed results but requires fewer assumptions and allows a more direct comparison of cultural change. Shifting the unit of analysis from the culture to the event allows events to be compared with one another. A case study from the evolution of numerical notation systems shows the potential of rigorous diachronic methodologies to complement synchronic ones. Although synchronic analysis is highly useful for studying correlations between traits, diachronic analysis is far better for analyzing processes of change.