----- Original Message -----
From: Peter T. Daniels
To: qalam@yahoogroups.com
Sent: Thursday, January 16, 2003 5:37 PM
Subject: Re: Introduction / question


Stephen Chrisomalis wrote:

>> 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,

> Why is that? Did you read both Pettersson's chapter and bibliography,
> and O'Connor's chapter on "The Alphabet as a Technology"?

My apologies for being unclear. I have indeed found enormous value in WWS
for my thesis in general, but not specifically on the questions I have
regarding the history of the alphabetic numerals of Eastern Europe and the
Caucasus. Pettersson has only a brief paragraph about them, and no
references specifically on point.

> Did you find my "brief notice" of Gamkrelidze in *Language*? And, if you
> read Russian and Georgian, you should look into his bigger book on the
> same topic. The English is a translation/adaptation of (part of) the
> Russian section.

Unfortunately, I have no facility in either Russian nor Georgian.

>> and while some
>> grammars describe these systems, they don't discuss the historical
>> contexts of their use and decline.

> That would seem to be part of the history of mathematics rather than the
> history of writing; there are books in that area. What do you think of
> Ifrah's big one, which he calls a new edition of the earlier one?

I have a number of problems with classifying the history of numeration as
part of the history of mathematics, and prefer to regard it as an adjunct
field to the history of writing. In large part, this is because very few
numerical notation systems were ever used for anything resembling
mathematics - or even for arithmetic, for that matter. Most historians of
mathematics who deal with numeration evaluate systems solely on their
efficiency for doing computation, but the vast majority of numerical
notation systems (Egyptian hieroglyphs, Roman numerals, etc.) were never or
rarely used for doing arithmetic, but rather for simple representation and
communication (record-keeping, dating, pagination, etc.)

As for Ifrah's book - The Universal History of Numbers (New York: Wiley,
1998), for those who may not know it - it is obviously the work of someone
who has put enormous effort into data collection - although even there, he
omits entirely the Glagolitic and Cyrillic alphabetic numerals I mentioned
earlier, among numerous other systems. His theoretical and historical
analysis is much, much weaker than his data collection - of course, this is
partly a consequence of his books being written for a popular audience.
Much of his theory is taken from Genevieve Guitel's Histoire comparée des
numérations écrites (Paris: Flammarion, 1975), which is particularly
egregious theoretically. I have many specific disagreements with him, but
they may not be worth going into here, since I suspect that few on the list
will have read his work.

Stephen Chrisomalis
Department of Anthropology, McGill University
schris1@...