Hello. I've been lurking on this list for about a
month, and over the past few days it's been swamped with a ton of OT
material. As I see it, I have two choices if I want to avoid this
material:
a) Leave the list.
b) Post something of my own, and hopefully
inspire some discussion.
I have chosen option b.
To introduce myself, I am an anthropology Ph.D.
candidate at McGill University. about three months away from my
defense. My research is a comparative historical study of all numerical
notation systems (visual but primarily non-phonetic techniques for representing
numbers) that have been used throughout history. My research topics, data
collection and methodology are closely affiliated with those of scholars of
scripts rather than those of the history of mathematics, which
only rarely concerns itself with written numeration. I'd like to think
that I have some small degree of expertise in this field, and that I can help
answer questions posed by people on this list, but I also recognize that as a
comparativist, I have a lot to learn from specialists in particular
scripts.
So, to start a discussion, I was wondering if
anyone is interested in alphabetic numeral systems. As many of you no
doubt know, a number of scripts (most notably Greek, but also Gothic,
Glagolitic, Cyrillic, Armenian, Georgian, Coptic, Ge'ez, Hebrew, Syriac, and
Arabic) assign(ed) numerical values to the letters of their scripts. To
simplify matters quite a bit, they work by assigning the values 1-9 to the first
nine letters, 10-90 to the next nine, and 100-900 to the next nine (using
obsolete or borrowed signs as necessary to fill out the full complement of
signs). They are thus additive rather than positional (place-value)
systems. All of them derive, directly or indirectly, from the Greek
alphabetic numerals, which were developed in the middle of the 6th century
BC.
I've been trying for years to learn about the
eventual fate of some of these systems. The Hebrew system is still
actively used in certain contexts, Greek to a minimal extent - sometimes
for pagination, and Coptic, Ge'ez and Syriac and Arabic in liturgical and
magical texts. However, as far as I can tell, the Glagolitic,
Cyrillic, Armenian and Georgian alphabetic numerals, despite surviving for many
centuries, are now all extinct. What I'm trying to figure out, so far without
success, is when they ceased to be used (if at all) and what historical
circumstances led to their discontinuation. For Armenian and Georgian,
it seems to have been during the period of Ottoman rule that they ceased to
be used, while I remember reading (sorry, no ref) that Peter the Great was
responsible for replacing the old Cyrillic system with Hindu-Arabic
numerals.
The best work I've been able to find on this
subject is Thomas V. Gamkrelidze's "Alphabetic Writing and the Georgian
Script" (Delmar, NY: Caravan Books, 1994), which despite its title is a
comparative work that is heavily focused on the historical relationships among
the alphabetic numerals and scripts of Eastern Europe and the Caucasus.
However, it is slight on historical data and information about texts, and seems
somewhat dubious on some other fronts. A. Schenker's "The Dawn of Slavic" (New
Haven: Yale, 1996) has lots of early historical information on Glagolitic &
Cyrillic numerals, but little for later periods. "The World's Writing
Systems" and other comparative studies of scripts have been of no help to
me on this topic, and while some grammars describe these systems, they don't
discuss the historical contexts of their use and decline.
If anyone has any expertise in the Eastern
European or Caucasian scripts, or knows someone who does, I'd greatly
appreciate any help you could provide. Otherwise, I'd be happy if people
just want to talk about this instead of ... well, anything.
Thanks, and kind regards,
Stephen Chrisomalis
Department of
Anthropology, McGill University
schris1@...