Stephen Chrisomalis

A Cognitive Typology for Numerical Notation

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.

Comparing Cultures and Comparing Processes: Diachronic Methods in Cross-Cultural Anthropology

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.

What's so improper about fractions? Prescriptivism and language socialization at Math Corps

Mathematical prescriptivism is a language ideology found in school mathematics that uses a discourse of rationality to proscribe language forms perceived as illogical or inefficient. The present study is based on a three-year ethnographic investigation of Math Corps, a community of practice in Detroit, Michigan, in which prescriptive language in the classroom is used both to highlight beneficial algorithms and to build social solidarity. Although motivated by the analogy with English orthographic reform, prescriptivism at Math Corps avoids potentially harmful criticism of community members of the sort often experienced by African American students. A playful linguistic frame, the prescriptive melodrama, highlights valued prescriptions, thereby enculturating students into the locally preferred register, the ‘Math Corps way’, which encompasses social, moral, linguistic, and mathematical practices and norms. A sociolinguistic and anthropological perspective on prescriptivism within communities of practice highlights positive alternatives to the universalizing prescriptions found in other English contexts. (Prescriptivism, language ideology, mathematics education, community of practice, Math Corps, linguistic anthropology, language socialization) *

The Cultural Challenge in Mathematical Cognition

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.

The Egyptian origin of the Greek alphabetic numerals

Traditionally, it has been assumed that the Greek alphabetic numerals were independently invented in the sixth century BC. However, the author finds a remarkable structural similarity between this system and the Egyptian demotic numerals. He proposes that trade between Asia Minor and Egypt provided the context in which the Greek numerals were adopted from Egyptian models.

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

ABSTRACT 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.

The perils of pseudo-Orwellianism

R. Alexander Bentley (2006) provides a provocative and timely challenge to archaeologists (and indeed to all scholars) in his quirky and tongue-in-cheek essay, ‘Academic copying, archaeology and the English language’ (Antiquity 80: 196-201). The dangers of sloppy, jargonfilled, and abstruse language are as great now as they were 60 years ago when Orwell’s essay ‘Politics and the English language’ (1946) was written. Yet the data Bentley provides concerning academic ‘buzzwords’ do not justify his conclusion that archaeology is in serious trouble when it comes to linguistic usage. Not only are there good reasons (aside from ‘random copying’) why such words are adopted and borrowed within and among academic traditions, they are not the primary contributing factor to the sloppiness and ambiguity against which Orwell and others railed. It is, as Bentley notes, hardly an exercise in futurology to predict that new buzzwords will emerge in academic writing. What he does not note (although he is surely aware of the fact) is that such words inevitably decline in popularity. One would, I suspect, be quite heartened if one were to compare ‘agency’ and ‘nuanced’ with similar buzzwords chosen from some decades ago. It is also worth noting, without denying that ‘agency’ and ‘nuanced’ are buzzwords, that virtually any word may be found to have increased enormously in usage in the ISI Web of Knowledge between 1986 and 2004. This occurs because of the very proliferation of journals that Bentley bemoans at the beginning of his essay, and in particular the proliferation of journals that are indexed in such databases. In Figure 1, I show the dramatic rise in the popularity of the non-buzzword ‘dirt’, starting (as with ‘agency’ and ‘nuanced’) in 1990. Because they do not account for the increasing size of online journal indices or the raw number of articles published in any given year, Bentley’s data thus fail completely to support his claim. Bentley’s choice of ‘agency’ and ‘nuanced’ as examples of buzzwords is curious. These are by no means the same sorts of words, and their purposes within the information system comprising the title, abstract and keywords of articles are entirely different. ‘Nuanced’ is rarely encountered in either title or keywords, but frequently in abstracts. It is a poor descriptor of an article’s topic. Unsurprisingly then, of the 454 instances of ‘nuanced’ in title, abstract or keyword in the ISI Web of Knowledge database from 1986 to 2004 (the period examined by Bentley), only 18 occur in the title of an article and none in keywords. While it is a neologism (though hardly brand-new; the Oxford English Dictionary notes its use in print in 1920), and has recently experienced a surge of popularity, it is not ambiguous and has no ready synonyms. Thus, while its appearance in English academic writing is certainly notable from a linguistic perspective and is interesting from a selectionist archaeological

Beyond teleology: ancient mathematics and social historyEleanor Robson. Mathematics in ancient Iraq: a social history. xxx+442 pages, 75 illustrations, 63 tables. 2008. Princeton (NJ) & Oxford: Princeton University Press; 978-0-691-09182-2 hardback £20.95.

The history and prehistory of the exact sciences has traditionally been the province of mathematicians, physicists and astronomers, using approaches that owe little to either history or archaeology (much less anthropology or linguistics). Such modes of analysis held as axiomatic the Platonic notion that mathematics was discovered rather than invented, and treated cultural variability in mathematics in terms of deviation from the ideal, which was held to reside in Western practice from Euclid onward. At best, the mathematics of ancient Near Eastern societies could be compared to the ‘Greek miracle’ by envisioning them as protoWestern, limited and tentative steps towards Truth, which could be treated in a handful of pages in history of mathematics textbooks.