Five great 2014 articles on number systems

The scholarship on numbers is, as always, disciplinarily broad and intellectually diverse, which is why it’s so much fun to read even after fifteen years of poking at it.  This past year saw loads of great new material published on number systems, ranging from anthropology, linguistics, psychology, history of science, archaeology, among others.  Here are my favourite five from 2014, with abstracts:

Barany, Michael J. 2014. “Savage numbers and the evolution of civilization in Victorian prehistory.The British Journal for the History of Science 47 (2):239-255.

This paper identifies ‘savage numbers’ – number-like or number-replacing concepts and practices attributed to peoples viewed as civilizationally inferior – as a crucial and hitherto unrecognized body of evidence in the first two decades of the Victorian science of prehistory. It traces the changing and often ambivalent status of savage numbers in the period after the 1858–1859 ‘time revolution’ in the human sciences by following successive reappropriations of an iconic 1853 story from Francis Galton’s African travels. In response to a fundamental lack of physical evidence concerning prehistoric men, savage numbers offered a readily available body of data that helped scholars envisage great extremes of civilizational lowliness in a way that was at once analysable and comparable, and anecdotes like Galton’s made those data vivid and compelling. Moreover, they provided a simple and direct means of conceiving of the progressive scale of civilizational development, uniting societies and races past and present, at the heart of Victorian scientific racism.

Bender, Andrea, and Sieghard Beller. 2014. “Mangarevan invention of binary steps for easier calculation.Proceedings of the National Academy of Sciences 111 (4):1322-1327.

When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition.

Berg, Thomas, and Marion Neubauer. 2014. “From unit-and-ten to ten-before-unit order in the history of English numerals.Language Variation and Change 26 (1):21-43.

In the course of its history, English underwent a significant structural change in its numeral system. The number words from 21 to 99 switched from the unit-and-ten to the ten-before-unit pattern. This change is traced on the basis of more than 800 number words. It is argued that this change, which took seven centuries to complete and in which the Old English pattern was highly persistent, can be broken down into two parts—the reordering of the units and tens and the loss of the conjoining element. Although the two steps logically belong to the same overall change, they display a remarkably disparate behavior. Whereas the reordering process affected the least frequent number words first, the deletion process affected the most frequent words first. This disparity lends support to the hypothesis that the involvement or otherwise of low-level aspects of speech determines the role of frequency in language change (Phillips, 2006). Finally, the order change is likely to be a contact-induced phenomenon and may have been facilitated by a reduction in mental cost.

MacGinnis, John, M Willis Monroe, Dirk Wicke, and Timothy Matney. 2014. “Artefacts of Cognition: the Use of Clay Tokens in a Neo-Assyrian Provincial Administration.Cambridge Archaeological Journal 24 (2):289-306.

The study of clay tokens in the Ancient Near East has focused, for the most part, on their role as antecedents to the cuneiform script. Starting with Pierre Amiet and Maurice Lambert in the 1960s the theory was put forward that tokens, or calculi, represent an early cognitive attempt at recording. This theory was taken up by Denise Schmandt-Besserat who studied a large diachronic corpus of Near Eastern tokens. Since then little has been written except in response to Schmandt-Besserat’s writings. Most discussions of tokens have generally focused on the time period between the eighth and fourth millennium bc with the assumption that token use drops off as writing gains ground in administrative contexts. Now excavations in southeastern Turkey at the site of Ziyaret Tepe — the Neo-Assyrian provincial capital Tušhan — have uncovered a corpus of tokens dating to the first millennium bc. This is a significant new contribution to the documented material. These tokens are found in association with a range of other artefacts of administrative culture — tablets, dockets, sealings and weights — in a manner which indicates that they had cognitive value concurrent with the cuneiform writing system and suggests that tokens were an important tool in Neo-Assyrian imperial administration.

Sherouse, Perry. 2014. “Hazardous digits: Telephone keypads and Russian numbers in Tbilisi, Georgia.Language & Communication 37:1-11.

Why do many Georgian speakers in Tbilisi prefer a non-native language (Russian) for providing telephone numbers to their interlocutors? One of the most common explanations is that the addressee is at risk of miskeying a number if it is given in Georgian, a vigesimal system, rather than Russian, a decimal system. Rationales emphasizing the hazards of Georgian numbers in favor of the “ease” of Russian numbers provide an entrypoint to discuss the social construction of linguistic difference with respect to technological artifacts. This article investigates historical and sociotechnical dimensions contributing to ease of communication as the primary rationale for Russian language preference. The number keypad on the telephone has afforded a normative preference for Russian linguistic code.

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