An anti-hiatus?

Apparently the English language has a lexical gap – it has no good term for ‘the end of a hiatus’ (‘resumption’ and ‘recommencement’ hardly suffice semantically), but, in any case, my apologies for having been largely absent here the past couple of months. Our department of nine full-time faculty has just finished three simultaneous job searches, which for those of you in academia, will give you a very good sense of what I’ve been up to.

And a very happy Pi Day (3/14) to all of you who celebrate! I didn’t do much special at 1:59 pm – perhaps I should have toasted Archimedes or something like that. I’m fonder of Pi Approximation Day anyway (July 22), since 3 1/7 is much closer to pi than 3.14.

This week’s World Wide Words (the e-magazine authored for 15 years by the inestimably talented lexicographer, Michael Quinion) featured one of my favourite numerical words, chronogram, meaning number-riddles in which a date is encoded in text using Roman numerals. Quinion mentions in passing the “three big books” of James Hilton from the 19th century, but this does little justice to the 1500+ pages of chronograms Hilton compiled over two decades. The first two volumes available for free download from Google Books (vol 1 – 1882; vol 2 – 1885; vol 3, 1895, is inexplicably only in ‘snippet view’).

Lastly, here is some good advice for those who are (rightly) considering charitable donations in support of victims of the Sendai earthquake.

Numeration and Numeracy in Cognition, Language, and Culture

Last month, at the Society for Anthropological Sciences annual meeting in Charleston, SC, I organized a panel of some really interesting material on the broad topic of numeration. I want to take this opportunity (again) to thank all the presenters for their attendance and hard work. The abstracts (as also published in the conference program) were as follows:

Toward a cognitive, historical, linguistic anthropology of numerals
Stephen Chrisomalis (Wayne State University)

For over a century, the study of numeration, number systems and allied topics has been a key part of the comparative study of thought, language, and culture. The anthropology of numbers and mathematics has traditionally been a locus for unilinear evolutionary thought linked to notions of primitivity. The papers in this panel constitute a call for a culturally-grounded cognitive science of numeration within four of the disciplines of cognitive science (anthropology, linguistics, philosophy, and psychology).

Recent research in language evolution, linguistic relativity, and cultural aspects of mathematical cognition draw attention to the need for anthropologists to re-engage with this new agenda. First, the cross-cultural study of numerals allows the investigation and evaluation of universal and particular aspects of numeration and their relationship with social organization. Because numerals have multiple modalities (e.g., verbal, graphic, gestural), examining patterns in number systems beyond linguistics allows us to evaluate to what extent number concepts can be separated from language, including universal grammar. Finally, just as the cognitive anthropology of plant and animal taxonomy contributes to ecological and environmental anthropology, the cognitive anthropology of numerals and mathematics underpins economic anthropology and the anthropology of science.

Spatial-numeric associations in literates and illiterates
Samar Zebian (Lebanese American University, Beirut Lebanon)

Several independent studies have reported a cognitive association between small numbers and the left side of space and larger numbers andthe right side of space among individuals who read and write from left-to-right (SNARC effect). These associations are reversed for individuals who read and write from right-to-left. The SNARC effect has widely been taken as evidence that numbers are conceptualized as points along a mental number line, however there is growing evidence that this systematic spatial performance bias related to writing directionality is an instance of strategic processing rather than a reflection of inherent spatial attributes of numbers. In an attempt to explain the “deeper” origins of these associations researchers are examining the linkages between number and finger counting. The current study examines whether finger counting practices reveal consistent spatial-numeric associations and whether there are any spillover effects to other tasks that involve object sorting and counting and other non-counting but quantitative tasks such as line bisection and speeded parity judgment. If, in fact, finger counting practices and not the directionality of writing set up spatial-numeric associations than we should be able to observe the same type of spatial biases in literates and illiterates. Preliminary evidence suggests that the finger counting practices of literates and illiterates are not same and furthermore that the spatial biases found in finger counting are not observed across tasks.

Zero’s beginnings: the Mayan case
John Justeson (SUNY, Albany)

This paper addresses linguistic and (Mayan) historical evidence concerning the origins of a numerical concept of zero. Comparative linguistic evidence suggests that zero is not part of basic numerical cognition; rather, it develops out of computing practices of mathematical specialists. Specifically, while zero is often assumed to be prerequisite to the invention of positional notation, it seems on the contrary to emerge as a notational device within such systems. This is clearly the case in Mesoamerica. A system of place-value notation arose in Guatemala and Mexico among Mayans and epi-Olmecs by 36 BCE, with no symbol corresponding to a zero coefficient. Although data is limited, circumstantial evidence is consistent with the following scenario for the emergence of a numerical zero: Mayan calendar specialists developed discourse practices, associated with calendrically-timed ritual events, that used the word “lacking”; the associated dates were represented in a new, non-positional system of notation, which replaced positional notation except in calculating tables; the sign for “lacking” was transferred from the new notation into these tabular positional notations; as a side effect of the algorithms that specialists used to add and subtract positional numerals, the “lacking” symbol was reinterpreted numerically.

Methodological reflections on typologies for numeral systems
Theodore R. Widom and Dirk Schlimm (McGill University)

Past and present societies worldwide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. In the present paper we provide a general framework
within which the efficacy of these typologies can be assessed relative to certain desiderata. Using this framework, we discuss the two influential typologies of Zhang & Norman and Chrisomalis, and present a new typology which takes as its starting point the principles by which numeral systems represent multipliers (the principles of cumulation and cipherization), and
bases (those of integration, parsing, and positionality). We argue with many different examples that this provides a more refined classification of numeral systems than the ones put forward previously. We also note that the framework can be used to assess typologies not only of numeral systems, but of many domains.

Social relationships as a lexical source for numeral terms in Amazonia
Cynthia Hansen and Patience Epps (The University of Texas at Austin)

Due to the relatively high degree of etymological transparency found in the numeral systems of Amazonia, it is possible to see the range of lexical sources from which the numeral terminology emerges. In this paper, we present the range of strategies used to create numeral terms below 5, based on an extensive survey of the numeral systems of close to 200 Amazonian languages conducted by the authors. More specifically, we discuss a strategy that is well-attested in Amazonia but that is not attested elsewhere in the world: a ‘relational’ strategy where terms for 4 (and sometimes 3-10) are built using a social relationship term, such as ‘sibling’ or ‘companion’. We propose that this strategy mirrors a gestural counting strategy found throughout the region where fingers are grouped in pairs.

Cultural variation in numeration systems and their mapping onto the mental number line
Andrea Bender and Sieghard Beller (University of Freiburg)

The ability to exactly assess large numbers hinges on cultural tools such as counting sequences and thus offers a great opportunity to study how culture interacts with cognition. To obtain a more comprehensive picture of the cultural variance in number representation, we argue for the inclusion of cross-linguistic analyses. In this talk, we will briefly depict the specific counting systems of Polynesian and Micronesian languages that were once derived from an abstract and regular system by extension in three dimensions. The linguistic origins, cognitive properties, and cultural context of these specific counting systems are analyzed, and their implications for the nature of a (putative) mental number line are discussed.

Retractions in anthropology

An editorial in the British Medical Journal earlier this week described Andrew Wakefield’s controversial 1998 Lancet article linking the MMR vaccine with autism as an “elaborate fraud”. Although the article was retracted in 2004 by ten of Wakefield’s co-authors, Wakefield himself continues to insist on its validity, despite new evidence presented by the journalist Brian Deer in the BMJ that the study was not simply flawed but that data were fabricated by Wakefield in a way that could not possibly have been accidental.

I’ve been reading the academic blog Retraction Watch for a few months now, and find it interesting for more than just the Schadenfreude that comes from seeing others go down in flames, because of the ethical meta-commentary that accompanies notices of retractions, and because it has made retractions much more prominent than any one journal could (except presumably the highest-tier ones). But that leads me to think: can anyone name cases of retraction in anthropological publications? I’m not talking about Piltdown-style refutation without retraction, or disputes such as Mead vs. Freeman or Chagnon vs. Tierney, or of anthropologists publicly changing their minds about earlier publications. Obviously in a non-experimental science we wouldn’t expect them at nearly the rate or in the same circumstances, but surely there must be cases of blatant plagiarism or ethical dishonesty that have resulted in a formal retraction … right?

Does anyone know of a list of anthropological publications that have been formally withdrawn from the academic record? Or, can anyone name some?

From ancient to digital archives

Belatedly, I note that Numerical Notation features prominently in the annual report of the Persepolis Fortification Archive Project published online last month (the section on my book is near the end). Matt Stolper, the head of the project, graciously gave me permission to reprint the Old Persian cuneiform tablet Fort. 1208-101 in my book, as it features the first evidence of the Old Persian numerals for the higher hundreds (in the numeral phrase ‘604’), and is the only known Old Persian document that serves an administrative function. Ultimately, the tablet was chosen by my editors to grace the extremely attractive cover.

Stolper alludes indirectly in the report to the serendipitous inclusion of this tablet in my research. I’ll be more direct: online publication and open access to the research findings of the Archive are the only reason I was able to integrate this important artifact into my research, at what was a fairly advanced stage of publication. If Stolper and his co-author Jan Tavernier had not published their findings directly online (Stolper and Tavernier 2007), enabling me to rapidly track it down once the media began to report on the tablet’s analysis, I could never have discussed it. (I should also give full credit to my wife, who first alerted me to the news articles on Fort. 1208-101). There are other arguments, such as cost, in favour of this model of publication, but access and speed – especially in fields like this, where data can lie unpublished for decades – are absolutely critical.

Romeyka

Happy New Year! I’m not a believer in new year’s resolutions but I do intend to post more frequently here over the next couple of months, at least with news items of interest.

Check out this interesting article in the Independent yesterday presenting Ioanna Sitaridou’s claim that Romeyka, an endangered dialect of Pontic Greek still spoken by around 5000 Muslim Greeks on Turkey’s Black Sea coast, preserves features of archaic Greek not known in any other modern variety. For instance, Romeyka preserves the use of the infinitive in various contexts in which you would never find it in standard Greek, or (apparently?) even in the Pontic Greek spoken in Greece and the diaspora. Sitaridou is completely correct in noting,”What we don’t yet know is whether Romeyka emerged in exactly the same way as other Greek dialects but later developed its own unique characteristics which just happen to resemble archaic Greek.” There doesn’t appear to be a formal publication associated with this article, but I’ll be looking out for one.