(1) The web page I cited was chosen purely in order to let list members see what the rod numerals looked like. Its statements about the nature and usage of these numerals should not be taken as authoritative. Better accounts are to be found in Chinese histories of mathematics, such as that of Li Di æèãZhongguo shuxue tongshi äåæåéåãNanjing 1997, pp 53 ff., in which their origins and early usage are discussed. Accessible and readily available English language discussions include HO Peng-Yoke, Li Qi and Shu: an Introduction to Science and Civilisation in China, Hong Kong 1985 rep. New York 2000, 55-58, and 92-104, and as part of the magisterial work by Joseph Needham, Science and Civilisation in China, volume 3, Cambridge 1959, pp 5-17, 45, 62 and 129-133.
(2) The Unicode home page says: "The Unicode Standard defines codes for characters used in all the major languages written today. Scripts include the European alphabetic scripts, Middle Eastern right-to-left scripts, and many scripts of Asia. The Unicode Standard further includes punctuation marks, diacritics, mathematical symbols, technical symbols, arrows, dingbats, etc.". I suggest that in an enterprise so universal and cross-cultural as Unicode, the definition of what counts as a "mathematical symbol" has to be conditioned by actual mathematical practice in the culture whose script is being encoded. We cannot simply take modern western mathematics as the standard. This means we have to look at the usage of Chinese mathematical writers in the periods in which rod numerals are used (and indeed this is the implication of John Jenkins' very sensible approach in his message).
(3) The most sophisticated indigenous Chinese mathematical texts before contacts with Western techniques (which did not, by the by appear obviously superior when the Chinese first met them in the 17th century) come from the algebraists of the late Song and Yuan periods (13th-14th centuries AD). The historian of science George Sarton characterised one of these, Qin Jiushao, as "one of the greatest mathematicians ... of all times". Qin developed methods for solving problems which would in western terms involve equations of up to the power 10. To do this he made use of a matrix notation in which rod numerals were essential. Needham (p. 131,132) reproduces pages from the work of two of Qin's contemporaries in which rod numerals appear in the text: the second example is particularly striking as showing a sequence of normal written characters with the rod numerals used as ordinary numbers. At a much more demotic level, Li Di (pp. 389 ff discusses and illustrates a mathematical MS from the Dunhuang cave shrines (possibly dating 7th-10th C.) in which rod numerals and common characters are mixed. On this basis, I suggest it is reasonable to allow that in Chinese terms the rod numerals should at the very least be admitted into the category of "mathematical symbols, technical symbols, arrows, dingbats, etc." , and personally I should urge that they should be accepted as a technical way of writing numbers - which is how they frequently functioned.
I hope this helps to advance the discussion. Further comments would be welcome.
Christopher Cullen
On 13 Jan 2004, at 01:45, Kenneth Whistler wrote:
John Jenkins responded:
Personally, I think it's an excellent idea.
I have my doubts, personally, but concur that getting a proposal together to debate the merits is a good idea.
It'd be good to get it on the UTC agenda for next month, so if you could start on the form. I can give you any help you need.
On Jan 10, 2004, at 5:23 AM, Christopher Cullen wrote:
These represent the arrays of "counting rods" on a counting board as
used in China for complex calculations before the invention of the
abacus. There are eighteen forms in all, representing the numerals
one to nine in two forms which are basically versions of each other
with a 90 degrees rotation. One form is used for units, the the other
for tens, then back to the first form for hundreds, and so on. A zero
is represented by a gap in the array. For pictures of these and an
explanatory text, see:
http://www.math.sfu.ca/histmath/China/Beginning/Rod.html
This page does show a few exhibits of tally marks scratched on earthenware, presumably using the same system as the counting rods. But what is lacking here are actual instances of these rod numerals used as characters in writing. The claim is that "Computations were actually done using rod numerals." But these are only shown in summary figures demonstrating the rod numerals used. Such figures are arguably graphics, not characters. The numerals are mathematical entities in the calculation method, to be sure, but the cited Sun Tzu Suan Ching talks about the calculations using rods, but doesn't actually *write* them in text. The discussion of the calculations is in terms of the ordinary Chinese number characters.
It would be a great convenience to have these as a standard resource rather than having to create a special private font in order to represent them.
The issue comes down to whether we are talking about characters in text, or whether we are talking about some glyphs representing the usage of counting rods, which might be more convenient if available in fonts, rather than being manipulated as graphics embedded in text.
The proposal will need to make the case for encoding *as characters*.
That said, clearly space for encoding is not an issue, of course, for a set of 18 of these things. Character properties, however, may be a problem, and should also be taken into account in any proposal.
The obvious precedent for a set of numerals like this are the Aegean numerals, U+10107..U+10118, which are also quite obviously derived from layouts of tallying sticks, and which have a units set 1-9 and a tens set 10-90 oriented at right angles to the 1-9 set. But the Aegean system used other counters for 100 and up, so there is not a problem of alternating values.
My suggestion would be to just give values 1-9, 10-90 for the Chinese rod numerals and be done with it, for the Unicode character properties. But the fact that the values are position dependent raises the suspicion that this really is a calculation system, rather than simply a set of 18 numeral characters, and as such, it may be over the edge of what is appropriate to encode in the Unicode Standard.
--Ken
From a private source, I have been told that these forms are neither
in any current Unicode encoding initiative, nor indeed anywhere in the
proposal pipeline. I should therefore be grateful for any comments or
advice that might guide me towards making a formal submission.
