Numerals inside the Great Pyramid

A couple of weeks ago all the news was about some new red ochre markings found in a shaft on the interior of the Great Pyramid at Giza (a.k.a. the Pyramid of Khufu), identified using an exploratory robot. That was pretty cool. But if you’re a professional numbers guy (as I am) you’ll be doubly excited to learn that it is probable that those marks are hieratic numerals. If this interpretation is correct, these are almost certainly mason’s marks used to indicate some quantity involved in the construction. Other than the fact that I would like all news outlets to stop calling them hieroglyphs (they aren’t – the hieratic script is a cursive Egyptian script that differs significantly from the hieroglyphs, and the numerals look nothing alike), this is really cool. I do want to urge caution, however: this does not imply that the Great Pyramid was designed along some sort of mystical pattern or using some numerological precepts. It actually doesn’t tell us even that the marks indicate the length of the shaft (as Luca Miatello suggests in the new article) – it could just as easily be 121 bricks in a pile used to make a portion of the pyramid. I am also not 100% convinced of the ’121′ interpretation – the 100 could be a 200, very easily, or even some other sign altogether, for instance. But the idea that numerical marks using hieratic script would be made by the pyramid-makers is entirely plausible and helps show the role of hieratic script in the Old Kingdom. Although it’s hardly going to revolutionize our understanding of Egyptian mathematics, it may well help outline the functional contexts of the use of numerals in Old Kingdom Egypt.

Pseudo-writing in the news

I promise I didn’t plan it this way – if I’d known about the article I’d have included it in my post earlier this week – but there’s a good short piece on pseudo-writing in New Kingdom Egypt at Past Horizons, about work being done by Dr. Ben Haring. At the workers’ village of Deir el Medina, one of the richest sources of our knowledge of daily life in the New Kingdom, ordinary (cursive, hieratic) script is found alongside a nonlinguistic system of marks used by tomb makers as personal marks of identity, and many writers were familiar with and used both systems, thus refuting the notion that pictograms are supplanted once phonetic writing comes along. The question of influence of hieratic script on this system of marks, and vice versa, is a rich line of intellectual inquiry.

Shady Characters

In all the hurly-burly of the past couple of months, I completely neglected the birth of a fascinating set of essays in progress at Shady Characters, a new blog by Keith Houston about the history and social context of punctuation. This is a subject on which I have blogged occasionally (e.g. A biography of the ampersand or A typology of quotation marks) but so far, Mr. Houston puts my efforts to shame. Of particular note is his three-part essay on the pilcrow (paragraph mark):

Part 1
Part 2
Part 3

Check it out!

Pseudo-writing at the zoo

Yesterday I went with my wife and son to the Detroit Zoo, which is a great place to visit if you’re ever in southeast Michigan, and especially on a wonderful warm sunny day like yesterday. Of course, while there, I took the requisite photos of animals doing stupid things, as well as family members posing in front of the aforementioned animals. But, being who I am, I also took some other photos, including this one:

Of course, the hieroglyphs aren’t real (the B and Z in the right-hand section of text are a dead giveaway), but they are also clearly meant to look Egyptian, and to be integrated with a piece of artistic representation, also clearly meant to look Egyptian. And, while it clearly does not follow the principles of decorum described by John Baines (2004) as characterizing the Egyptian artistic and epigraphic tradition, no modern observer could mistake this for anything else other than an attempt to emulate Egyptian art and writing.

The Egyptian hieroglyphs are surely the most thought-about and talked-about ancient writing system in the Western social imagination of the past five hundred years. (One could argue, I suppose, that this honour should go to the Chinese writing system, but ‘ancient’ doesn’t really apply.) The esoteric and foreign-yet-ancestral nature of Egypt with relation to Western civilization, and in particular its hieroglyphic script, led to it being important both in early modern European thought (Iversen 1993) and in 19th century American thought (Irwin 1983). Virtually every inhabitant of modern Western societies learns something about what hieroglyphs are supposed to look like, as in the Simpsons episode “Simpsons Bible Stories”:

Skinner: All right, read me back what I have so far, Mrs. Krabapatra.
Krabappel: Bird, bird, giant eye, pyramid, bird.
Skinner: Mmm-hmm, very good. Uh, giant eye, dead fish, cat head, cat head, cat head, guy doing this …
[strikes the "walk like an Egyptian" pose]
(Source: http://www.snpp.com/episodes/AABF14)

The photo above, and the Simpsons example, are examples of pseudo-writing: characters that have the appearance of writing (whether a specific writing system, or just writing in general) but are not intelligibly readable in any script. In other words, pseudo-writing is drawn to look like writing, but does not convey linguistic information. I have a longstanding interest in pseudo-writing, and maybe if I feel energetic will get around to writing an article on the subject someday.

In ancient contexts, such as Early Dynastic Egypt (Baines 2004) or Minoan Crete (Whittaker 2005), pseudo-writing was used mark prestige or status without requiring an actual text to be read – it sufficed to have something that looked like writing to obtain the social benefits of possessing a written text. In an era with perhaps 1% literacy, those benefits could be considerable – it was the presence of writing, rather than its use to convey information, that mattered most in these contexts. Pre-literate children who are aware of what writing is, but are unable yet to write, engage in writing-like activities, basically organized scribbling, in emulation of and in preparation for actual literacy (Tolchinsky 2003). In typography, “lorem ipsum” text contains bits of Latin, but is certainly not meant to be read – its purpose is to serve as a placeholder and words are freely added and broken up. You can interpret Hanzi Smatter-like practices of tattooing gibberish or simply incorrect Asian characters on unknowing Western bodies as pseudo-writing. The Voynich Manuscript (about which I have apparently become a bit of an expert) is, in my opinion and that of many others, a very clever piece of pseudo-writing designed to be unreadable, and thus undecipherable, and thus valuable. And, perhaps one of my favourites, since it was discovered by me and my student Katherine Tong in a classroom project, is ‘THE MR MAROR TO BE JOLLY LA LA LA LA LA‘ and other nonsensical micro-text (less than 1 mm high) used decoratively on discount holiday-themed ceramics – unless you looked very closely, you would see only that there was writing, not what it said (Tong 2008). So its purposes can be quite varied, depending on the context.

At the zoo, the purpose of the hieroglyphic pseudo-writing was clearly to index Africanness – it was found in the area of the zoo with many African animals. This is heartening, insofar as Egypt is frequently considered to be not really African and thus part of the politics of excluding Africa from civilization. I don’t know anything about the artist, but it sure beats a blank wall. I suppose I do wish someone had taken the time to use some actual Egyptian text, but then I wouldn’t have had anything to write about.

References
Baines, John. 2004. The earliest Egyptian writing: development, context, purpose. In The First Writing: Script invention as history and process, Stephen Houston, ed., 150–189.
Irwin, John T. 1983. American hieroglyphics: the symbol of the Egyptian hieroglyphics in the American Renaissance. Johns Hopkins University Press.
Iversen, E. 1993. The myth of Egypt and its hieroglyphs in European tradition. 2nd ed. Princeton University Press.
Tolchinsky, Liliana. 2003. The cradle of culture and what children know about writing and numbers before being taught. Psychology Press.
Tong, Katherine. 2008. THE MR MAROR TO BE JOLLY LA LA LA LA LA: An investigation of writing
(and gibberish) on Dollarware. Dollarware Project, report 17. http://dollarware.org/report17.pdf.
Whittaker, Helene. 2005. Social and symbolic aspects of Minoan writing. European journal of archaeology 8 (1): 29-41.

Uncle Jerrold and the schwa

Yesterday as I was wandering out of the parking lot on campus, waiting for the caffeine to kick in before another 9am meeting, I stumbled by the same newspaper box I always do, when I saw a giant schwa staring back at me. A local alternative paper, the Metro Times, has an article on a Detroiter who goes by the name ‘Uncle Jerrold’ and his campaign to introduce the schwa as a new letter of the alphabet. The article here is a fascinating read, not because it’s likely to become a reality but because of the ways in which the logic of orthographic reform relates to beliefs about language and cognition.

Writing systems and literacy: a syllabus

At the end of a conference a few years ago on writing systems, we (the dozen or so participants) energetically promised to share with one another the various syllabi we use in our courses on writing systems and literacy. Apparently we failed, as I have been unable to find any correspondence indicating that we did so. I taught such a course to a small group of seniors in the fall of 2006, and this fall I am teaching a highly revised version of the course to a small group of grad students. I don’t think the syllabus itself is anything special (it’s a seminar: we read a lot, then write long papers), but below, I give the reading list along with a brief discussion of each:

1. Andrew Robinson, Writing Systems and Literacy: A Very Short Introduction.
None of my students have any particular prior expertise in the area, so I’m having them read this prior to our first class meeting. It is what it is, but will form a really good introductory set of ideas for them.

2. Maurice Bloch, How We Think They Think: Anthropological Approaches to Cognition, Memory, and Literacy.
This is a great mix of theory from social and cognitive anthropology and the detailed ethnographic work in Madagascar that Bloch is known for, linking literacy to memory and cognition in some really intriguing ways.

3. John Chadwick, The Decipherment of Linear B.
I used this in the first incarnation of the course – a fantastic autobiographical account of the world’s most famous script decipherment, and a grand tribute to Michael Ventris, whose tragic death marks the narrative indelibly.

4. John Defrancis, The Chinese Language: Fact and Fantasy.
While the title suggests that it is more generally on language, the core of the book is on the nature and social context of the Chinese characters, ranging from basic semiotic issues to modern romanization efforts, and the gross misunderstandings most Westerners have of the script.

5. Jack Goody, The Domestication of the Savage Mind.
Goody isn’t as popular today as he was twenty years ago, but I find his account extremely compelling and theoretically rich. The critics get their day (see below) but fundamentally my approach to numerical notation rests on Goody, another holdover from the first incarnation of the course.

6. Stephen Houston (ed), The First Writing: Script Invention as History and Process.
Finally out in paperback so I can assign it – this collection of magisterial essays is social, historical, linguistic, and archaeological, framing the origin of writing in a thoroughly anthropological framework.

7. Sylvia Scribner and Michael Cole, The Psychology of Literacy.
Despite the title, this is a work of deep ethnography as well as cross-cultural psychology, investigating what effects (if any) the native Vai syllabary and other scripts have on a complex Liberian literate context.

8. Brian Street, Literacy in Theory and Practice.
I suppose this would be the ‘anti-Goody’, placing literacy (correctly) as a social practice whose cognitive effects cannot be predicted. Street’s theoretical position forms the mainstream of the modern anthropology of literacy.

9. Peter Wogan, Magical Writing in Salasaca.
A great little ethnography injecting issues of inequality and colonialism, as well as ritual and religion, into the literate lives of the people of Salasaca in Ecuador (I’m also assigning this because we have two Ecuador specialists in our department).

10. Niko Besnier, Literacy, Emotion and Authority: Reading and Writing on a Polynesian Atoll.
A last-minute addition, a further ethnography allowing us to look at another region of the world, but also to look at the ways in which literacy relates to the construction of individual identities and personal authority.

Why paleography matters: solution

Well, we haven’t had an answer, so I’ll give it to you:

Solution: Plate adapted from Jenkinson 1926: Figure 10.

All of the numeral-phrases except the bottom right read CXLVII (= 147). I’ve highlighted every other character in red to emphasize the distinct characters, making this solution comprehensible if not obvious. The fact that you, my readership (several of whom have training in paleography) couldn’t find the solution even after two clues demonstrates the ongoing importance of paleography as a scholarly profession, and also demonstrates the highly aberrant character of the hand.

This plate is taken from a 1926 article ‘The use of Arabic and Roman numerals in English archives’ by Sir Hilary Jenkinson, the doyen of British archivists (and who, shockingly, lacks a Wikipedia page!), who was also one of the major figures in early-twentieth-century British paleography (Jenkinson 1915, 1926). Jenkinson writes of this plate:

First there is the unimportant but highly curious development in one or two Courts of a special Roman numeration for the membranes of their Rolls, which in its later stages is practically unreadable. Our illustration (fig. 10) shows the number 147 as it was written in the years 1421, 1436, and 1466 and finally the number 47 as it appears in 1583: it does not show the worst that might be selected and is only half the size of the original (Jenkinson 1926: 274).

Although I have been familiar with this plate for over a decade, for the life of me I can’t find a way to read 47 (XLVII) out of the bottom-right phrase. I’m sure that Jenkinson had some grounds (probably contextual) for believing this to be the numeral, but I just can’t get 47 out of it. Weirdly enough, I can find 147 in it, but that may just be a product of its association with the other three phrases. Note that the other three are chronologically close while the fourth is nearly a century later. Anyway, I’m really stumped on this one.

But I actually wish to disagree with Jenkinson on one word: ‘unimportant’. The cursive transformation of cumulative numeral phrases is important in the history of numeration because it is the most common means by which cumulative systems, which rely on the repetition of like symbols whose values are added (e.g. XXX = 30), turn into ciphered systems, which do not do so. The figure below (borrowed from my book) shows how the Egyptian hieroglyphic numerals for 6, 9, and 300 became paleographically reduced over time into hieratic forms that do not show any evidence of their original cumulative structure. The ligaturing of individual signs eventually leads to the reconceptualization of the entire set of signs as a single unit. In fact, this process occurred (slightly differently) with the Brahmi numerals 1 through 3 of ancient India, which eventually became the ciphered figures of the Indian, Arabic, and Western numerals used by virtually everyone today (see this chart, for instance).

Cursive reduction of Egyptian numerals (after Chrisomalis 2010: 47)

The Roman numerals ceased to be used in manuscript-writing throughout early modern Europe, so there was no opportunity for the form of this particular court hand to lead from extreme cursivization to something structurally distinct in the Roman numerals. But it could have happened, just as it happened before several times. And that (along with so many other things) is why paleography matters.

Chrisomalis, Stephen. 2010. Numerical Notation: A Comparative History. New York: Cambridge University Press.
Jenkinson, Hilary. 1915. Palaeography and the practical study of court hand. Cambridge: Cambridge University Press.
Jenkinson, Hilary. 1926. The use of Arabic and Roman numerals in English archives. The Antiquaries Journal 6:263-275.

Dresden Codex online

From David Stuart’s Maya Decipherment blog, news that the Saxon State Library of Dresden has published hi-res colour images of the Dresden Codex online. It is, of course, the most detailed and complex surviving account of Maya mathematical astronomy and an extraordinarily important document for our knowledge of Mesoamerican exact science.