Up to 11, up to 100

On the weekend my wife and I took the opportunity to rewatch the finest rock/mock-umentary ever made, This is Spinal Tap (sorry, Unicode still hasn’t got around to n-diaeresis). We’re going to see the boys from Spinal Tap / every other Christopher Guest movie ever made, unwigged and unplugged, in concert in Detroit on the 29th, so this was sort of preliminary research.

As you know if you’ve been reading for a while, or at least if you’ve been reading and paying attention, I study cultural aspects of numbers and mathematics, and so today I’d like to talk to you about one of the greatest phrases coined in the past quarter-century, ‘up to eleven’ – check out this strikingly long list of pop-cultural references as evidence of its ubiquity, or just so you know what I’m talking about here if you’re unfamiliar with the movie. The core idea is that a higher number represents more (in this case, more volume –> better!), rather than simply being a more fine-grained division of a continuum (i.e., 1 to 10 –> 1 to 11 –> … 1 to 100, etc.).

Okay, it’s hilarious, and I’m making it sound all technical and such, but I have a point here. It’s an example of what I call conspicuous calculation, the use of (often unnecessarily) large numbers for discursive effect. This is highly prevalent in Western societies, but is by no means limited to them – one of the earliest pieces of Egyptian text, the Narmer mace-head, contains a set of numerals ranging into the millions boasting of a large quantity of livestock and people taken as plunder. Particularly in state societies that have a focus on quantification and enumeration, numbers can become a tool to overawe, manipulate, and obfuscate. The argument is longer (and still in development), but you get the idea.

But in one of those fantastic serendipities, a fascinating article came out in the New York Times a few days ago, ‘Confused by SPF? Take a Number‘ by Catherine Saint Louis. It’s a fascinating look at how an objective measurement (Sun Protection Factor / SPF: the measured ratio of the time it takes to burn with sunscreen on to the time it takes to burn without it) can be used as part of a rhetorical advertising war and can exaggerate the actual protection you are receiving. Although dermatologists are aware that there is little practical difference between SPF 30 and SPF 100 – and that far more significant factors include how much sunscreen you use, and how thoroughly you apply it – the numbers war has significant effects, as discussed in the article:

“It captures the consumers’ attention, the high SPF,” said Dr. Elma D. Baron, an assistant professor of dermatology at Case Western Reserve University who sees patients at hospitals in Cleveland. “Just walking down the drugstore aisle and seeing a SPF 90 or 95, they assume, ‘This is what I need.’ ”

and

When told of Neutrogena’s 100+ lotion, Ms. Bigio worried that the sunscreen she always wears when rock climbing and bicycling to work isn’t enough. “It makes me feel like SPF 45 is inadequate,” she said.

Now that there is such a thing as SPF 100, there is a real danger that 100 will be interpreted as complete protection. Living in a decimal society permeated by scientific discourses, we tend to associate 100 with 100%. It’s no coincidence that the new Neutrogena product is advertised as SPF 100+, not SPF 104 or SPF 106.4. In contrast no one would advertise SPF 25 as ’20+’. The spurious roundness of the number allows the consumer to associate 100 with completeness and thus to be confident of full protection. But SPF isn’t a measure of the percentage of the sun’s rays blocked, and it doesn’t have an upper limit.

When I was a kid, we had SPF 6 or SPF 8 around the house, and we rarely wore it (even though I’m pretty pale for someone of partially Mediterranean heritage, and one half of my family is particularly burn-prone). Was I well-protected? Probably not. I also should have been wearing a hat (still to this day I am a non-hat person). Today you can’t even find such low SPFs anywhere, and you will find people who think that putting anything less than SPF 30 on your child is tantamount to abuse. But make no mistake: this is a discursive battle as much as it is a scientific one, one ultimately governed not by laboratory practice but by the need of an industry to outmanoeuver competitors, literally, by outnumbering them.

Medieval anthropology

At the International Medieval Congress this past weekend, I had the very unusual experience of being (as far as I am aware) the only representative of my discipline at a conference with over 3000 attendees (although there were plenty of linguists around, and at least some medieval archaeologists). A good time was had by all – well, at least by my wife (an actual medievalist) and myself and our friends. My paper (longer discussion to follow) was very well attended and well received, and initiated some interesting discussions.

My work on numerals is hyper-specialized, to say the least. There are maybe five or eight living anthropologists, worldwide, whose work is centrally about numerals, and perhaps a couple of dozen linguists on top of that. Of course there are people who have written about numerals other than these, but they are not specialists in the topic. But while my core research is hyper-specialized, I think of myself, by contrast, as a polymath. I have graduate-level training in cultural anthropology, history (both ethnohistory and history of science), archaeology, cognitive science, and linguistics. And it makes me very, very happy to have this breadth. So there really aren’t too many situations where I feel extraordinarily out of place in humanities and social science-type conferences, and this one was no exception. If the opportunity arose to present there again, I would jump at the opportunity – despite the fact that by all rights, I don’t really belong there.

On Saturday I attended an excellent roundtable entitled ‘Medievalism across Time and Space’ hosted by my friend Julie Hofmann, which dealt with the definition of the medieval both in scholarly discussions of different time periods and different regions, as well as in how the public perceives and understands ‘the medieval’. Ambitious, no? Also really fascinating stuff. In the middle of this discussion, someone made a comment that made me realize that of all times and places, North American anthropology really excludes ONLY the medieval from its purview. There are dozens of archaeologists trained jointly in anthropology and classics departments, and/or who teach interdisciplinarily in both fields. Hundreds of classical archaeology students every year get their archaeological training primarily in anthropology departments. Similarly, there are hundreds of early modernists in anthropology: people who focus on Spanish colonialism in the New World, for instance, or world-systems theorists, or people interested in Atlantic World / diasporic studies. But the medieval is almost entirely out of our grasp.

This is an odd gap, to say the least, for a discipline that purports to be a holistic comparative study of human behaviour. At the panel it was noted that in many small (and not-so-small) history departments, medievalists get the honour (???) of teaching Western civilization courses that start with Sumer (anthropological archaeology has numerous specialists) and end with the twentieth century (which the vast majority of cultural anthropologists have expertise in). And it’s not at all that I think that somehow this means I, or any other anthropologist, would do a better job than a medievalist would of teaching such a course, nor that I would want to do so. But if I were going to construct a ‘world survey’ anthropology course, it would be very challenging to come up with relevant material written by anthropologists or anthropologically-trained archaeologists that focuses on the millennium of history in which medievalists specialize. But I can’t think of any valid conceptual or methodological reason to exclude the medieval from the anthropological.

But it also occurs to me that, despite it not being a formal part of my training, I do have a lot of experiences, skills, and knowledge pertinent to medieval studies. I have two years of Latin. My wife is a medievalist and through osmosis, I know almost as much about her area of specialty as she does about mine. The first paper I ever wrote in grad school was on the historical ecology of the early Icelandic state, and I even once thought seriously about looking at the post-Roman archaeological record in Britain from the perspective of postcolonialism as my dissertation (little known secret, until now!). About 10% of my book (at least) deals with medieval Europe and the Middle East, and if you count the rest of Asia in there, more than that. And of course, I spout off about the late medieval transition from Roman to Western numerals at virtually any possible occasion, because so many people think they know why it happened, and are so very, very wrong.

One of the central ideas tossed around in the roundtable was that ‘the medieval’ is a nebulous object, subject to both scholarly and popular imposed definitions that satisfy no one. It was noted by many that ‘medieval India’, ‘medieval Japan’, ‘medieval Islam’, etc. all refer to very different social configurations and chronological periods, and I chimed in that of course if there were a chronological definition then one really needed to include New World societies as well – recognizing fully that no one is happy with such a definition in any case.

So in my copious (ha!) spare time over the next couple of weeks, I’m going to put together a working bibliography of ‘medieval anthropology’: scholarly publications in social/cultural, linguistic, or archaeological anthropology that have as one of their central objects the Old World between roughly 500-1500 CE. Because I do know they’re out there, at least in limited quantities, and it seems like a real gap. The only things I want to exclude are a) physical anthropology; b) medieval archaeology as written by non-anthropological archaeologists, i.e. almost anyone trained in Europe.

So how about it: any anthropologists in the audience know of any material I should be including?

Edit (2010/01/31): I have now created this bibliography which can be found here.

Numbering by the books

On Thursday I will be pretending to be a medievalist at the International Medieval Congress in exciting Kalamazoo, Michigan and hoping not to get tossed out of the room for being a dirty no-good social scientist. My paper is entitled “Numbering by the Books: The transition from Roman to Arabic numerals in the early English printing tradition”, and is … well, it is just about what it sounds like it is, only significantly more interesting! I’m looking at the not-so-systematic introduction of Arabic (Western) numerals into the printing tradition, using England as a case study because there’s such a huge body of accessible texts (all hail the great god EEBO!), and commenting on the common wisdom that Arabic numerals allowed books to be organized more efficiently than Roman numerals, using a combination of quantitative and qualitative analysis.

The panel is being organized by my friend Shana Worthen and promises to be really excellent. For those of you who may be at K’zoo this year, it’s Session 74 (Fetzer 1035, Thursday 1:30pm). Hope to see you there!

Language and Societies

The students in my graduate-level linguistic anthropology course, Language and Societies, have written extended abstracts of their research papers, which we have now published at a new blog, Language and Societies. Both I and they would greatly appreciate any comments, questions, or suggestions you have regarding their projects, several of which go well beyond this course and will form the basis for ongoing research leading towards advanced degrees in linguistics or anthropology, and/or (one hopes) peer-reviewed publication. Please comment on the specific posts at the Language and Societies blog. Thanks!

Handbookery

Here are a couple of new publications of which I am very proud and which may be of interest to you. I’ve included them both lest the publishers involved think I’m playing favourites!

Chrisomalis, Stephen. 2008. The cognitive and cultural foundations of numbers. In The Oxford Handbook of the History of Mathematics, Eleanor Robson and Jacqueline Stedall, eds., pp. 495-517. Oxford: Oxford University Press.

Numbers are represented and manipulated through three distinct but interrelated techniques: numeral words, computational technologies, and numerical notation systems. Each of these has potential consequences for its users’ numerical cognition, but these consequences must be understood in terms of the functions and uses of each technique, not merely their formal structure. Most societies use numerical notation only to represent numbers, and have a variety of other techniques for performing arithmetic. The current Western practice of pen-and-paper arithmetic is anomalous historically. The transmission, adoption, and extinction of numerical systems thus depends primarily the social and economic context in which cultural contacts occur, and only minimally on their perceived efficiency for arithmetic.

Chrisomalis, Stephen. 2009. The origins and co-evolution of literacy and numeracy. IN The Cambridge Handbook of Literacy, David R. Olson and Nancy Torrance, eds, pp. 59-74. Cambridge: Cambridge University Press.

While number concepts are panhuman, numerical notation emerged independently only in state societies with significant social inequality and social needs beyond those of face-to-face interaction, and in particular with the development of written texts. This survey of seven ancient civilizations demonstrates that, although written numerals tend to develop alongside the first writing, the specific functions for which writing and numerals co-evolve are cross-culturally variable. A narrowly functionalistic approach that generalizes the Mesopotamian case to all early civilizations and proposes that numerals always emerge for accounting and bookkeeping is empirically inadequate. An alternate theory is proposed that regards the emergence of writing and numerical notation as an outgrowth of elite interests relating to social control, but leaving unspecified the particular domains of social life over which those elites use to control non-elites. Numerical notation is a special-purpose representational system that, in its simplest form, unstructured tallying, is a precursor to written communication, and which persists and expands as a parallel notation in literate contexts.