Category: Numerals

Zapotec decipherment on the horizon

Artdaily.org reports on a major new initiative to compile an epigraphic corpus and eventually (it is hoped) decipher the Zapotec hieroglyphic writing system. Unfortunately the article has been poorly translated, and I am at a loss as to the meaning of the sentence, “During that age, numeral system began, which would reach a great sophistication towards 7th century.” But that’s not the point. Most people who think of Mesoamerican writing think of the Maya hieroglyphs, or maybe, maybe the Aztec manuscript tradition. But the earliest inscriptions of the Valley of Oaxaca (the Zapotec homeland) are very early (500 BCE) – as early or earlier than any other Mesoamerican writing (with the exception of the enigmatic Cascajal Block) and (debatably) centuries earlier than any writing in the Maya languages. Monument 3 from San José Mogote is the earliest clear evidence for Mesoamerican numeration (used in the name ‘1 Earthquake’).

But we really don’t know as much as we would like about the Zapotec script (of which there are hundreds of examples dating from 500 BCE to 850 CE, although many are short or fragmentary). Our state of knowledge about the script is roughly where we were with Mayan writing forty years ago: we can read the numbers and the calendar, and we can ‘interpret’ a few other glyphs contextually, but that’s about it. There has been important recent work on Zapotec, particularly by Javier Urcid, whose excellent book, Zapotec Hieroglyphic Writing (2001), represents a major step forward, but it isn’t a decipherment nor does it claim to be. If a Zapotec decipherment or even a partial decipherment were to emerge from this new initiative, it would clearly help sort out many thorny phylogenetic issues in lowland Mesoamerican linguistic history and culture. But the script may not be highly phonetic, and certainly is not an excellent candidate for a Linear-B-Michael-Ventris style decipherment. Still, one can hope.

Cherokee petroglyphs?

My attention has been drawn to a recent article in the New York Times by John Noble Wilford, describing a purported cave inscription in the Cherokee script from Kentucky. If confirmed as accurate, this would be the oldest dated text in Cherokee, and almost certainly would have to be in Sequoyah’s hand or one of the earliest script learners. I’m on vacation right now and don’t have access to all the resources I’d normally have to do a detailed analysis, but here are a few principles to keep in mind as you read the article:

– The photo you see with the ‘characters’ has been highlighted in white in a way that would not be acceptable practice among epigraphers, due to the risk of misreading. We have no way of knowing with any certainty where the boundaries between different characters are.

– The dating is entirely on the basis of a portion of the inscription not shown, which apparently reads either 1808 or 1818 in Western (Arabic) numerals. But we don’t have any knowledge of whether Sequoyah (George Gist) had any knowledge of how to form Arabic numeral dates at this early period. And the fact that we can’t decide, apparently, if the third character is a 0 or a 1, even though the first character is apparently evident as a 1, suggests a problem with the paleography that should make us very wary of the validity of the finding.

– The inscription is not a text in the sense of something that could be deciphered; rather, the signs are a hodgepodge of Cherokee-like syllabic symbols. Kenneth Tankersley, the archaeologist who is making the assertion, argues that this was a sort of practice text, an ABC of the Cherokee syllabary. But this claim raises a warning flag for me – it raises the evidentiary bar needed to conclude that this is, in fact, Cherokee writing rather than some petroglyphs (or natural lines in rock, or a combination of the two) that can be seen to resemble some Cherokee signs post facto by modern scholars. It also makes me wonder why the early design of glyphs would be taking place bye engraving stone (a difficult medium) rather than something easier to work with.

– Even if the signs are (proto-)Cherokee syllabics, and even if the number 1808 or 1818 is written on it, this does not establish that this was the date of the inscription. The number could have a non-calendrical meaning. The number could have been inscribed at a different time from the other characters. The number could in fact have been written at any time in order to give the inscription an earlier date (for purposes of deception or otherwise).

– There are purportedly 15 identifiable Cherokee characters, but there are also many other characters in the cave that do not resemble Cherokee characters. We would need to know a great deal more about the entire sign-inventory before we could conclude that the resemblances were sufficient to identify them as early Cherokee signs.

– Janine Scancarelli, an expert on Cherokee syllabics who is quoted in the article, does not in fact comment on the validity of the interpretation, but simply describes what is known about the resemblance of Cherokee symbols to other symbol systems.

– There is no peer-reviewed research yet on this finding (although I’m hoping that some of you who were at the SAAs this year saw the talk).

Now I’m not saying at all that this is a hoax or fraud. We certainly don’t have any evidence of that. But we also don’t have any good evidence to convince me that this site is radically different from other petroglyphic sites from the 18th and 19th centuries, and certainly not that we have a dated instance of a proto-Cherokee inscription. I’m looking forward to more information coming to light on this very interesting find, nonetheless.

Obituary: Willard Walker

I learned some sad news today from the very small field of Native American writing systems and literacy studies. The linguistic anthropologist Willard Walker, whose prominent work on the Cherokee syllabary is the most serious scholarly study on the subject, passed away late last month. Dr. Walker, who was a professor emeritus of anthropology at Wesleyan University and was one of that department’s founders, was 82.

One of the more remarkable facts about literacy in colonial and pre-modern North America is the extreme paucity of independently developed writing systems and numerical notations. In contrast to West Africa, where there are dozens of examples of individuals creating indigenous scripts after being exposed to the Roman or Arabic scripts, there are relatively few indigenous North American scripts, and of these, the Cherokee syllabary (in which each sign encodes a syllable rather than a single phoneme) has been one of the most successful. Walker’s work was an effort to explain the development of Cherokee writing that was respectful to Sequoyah (George Guest), the script’s inventor, while steering clear of ‘great man’ fallacies and attempting to understand the sociocultural context of the script’s invention and acceptance (Walker 1969, 1984a, 1984b, 1985; Walker and Sarbaugh 1993). A major part of his life’s work was comparative, showing the ways in which Cherokee interest in literacy contrasted with grave ambivalence about the practice of encoding oral traditions in written texts among many other peoples of the Americas.

Over the years I’ve been asked numerous times to name my favourite numerical notation system. At first I thought that was just a bizarre question, but then, I figure that people in film studies must get asked what their favourite movies are all the time, and that people are just looking for a way into my subject area, a hook, if you will. So for the past couple of years, I’ve told them about the Cherokee numerals. My story here, which is one that Walker touched on only briefly, is that where the Cherokee syllabary thrived (and continues to thrive today), the numerals that Sequoyah developed were never accepted. While the syllabary is well-suited for writing the Tsalagi (Cherokee) language, the Western numerals sufficed for writing numbers, so the Cherokee council voted not to adopt them. They survive only in two documents in the Gilcrease Museum in Tulsa, Oklahoma – the only evidence we have for the creation of an indigenous North American numerical notation. Unfortunately, none of the standard texts on numerical notation currently published (ahem) mention them.

The other really neat thing about the Cherokee numerals is that they display a remarkable structural resemblance to the system of numerals used by the Jurchin of northeastern China, who developed a script in the 12th century, and who were later known (famously) as the Manchu when they ruled China. If you follow that link you see that the Jurchin system has special signs for 1-19, then every decade from 20-90, then signs for the higher powers of 10. There is no possibility that Sequoyah knew of this system – really, no one in the Western world did until the 1890s – but the Cherokee system parallels it in nearly every detail – although of course the signs are entirely different. If I were to make the case for cognitive constraints interacting with cultural and linguistic variability to produce remarkable and unexpected parallels, this would be a good example. Theoretically, then, the Cherokee numerals are extremely important even though no one actually used them, as far as we can tell.

I always thought that I might contact Dr. Walker to talk to him about the numerals, which he discussed only in passing. Certainly I would have been thrilled if he read the few pages of my book that I devoted to the subject and had anything to say about them. Alas, that will never happen now.

The clock in my office bears Cherokee numerals – some innovative person sells them through Cafepress. It is the only ‘text’ with the numerals readily available to anyone today. Tomorrow, in honour of the work of Dr. Walker, it will be silent.

Walker, W. 1969. Notes on native writing systems and the design of native literacy programs. Anthropological Linguistics: 148-166.
———. 1984a. The Design of Native Literacy Programs and How Literacy Came to the Cherokees. Anthropological Linguistics: 161-169.
———. 1984b. Literacy, Wampums, the Gúdabuk, and How Indians in the Far Northeast Read. Anthropological Linguistics: 42-52.
———. 1985. The Roles of Samuel A. Worcester and Elias Boudinot in the Emergence of a Printed Cherokee Syllabic Literature. International Journal of American Linguistics: 610-612.
Walker, W., and J. Sarbaugh. 1993. The early history of the Cherokee syllabary. Ethnohistory: 70-94.

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.

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!