Re: Chinese rod numerals

[Christopher Cullen]

My submission is that the evidence I cite does show that the rod 
numerals were used in writing.  Of course some forms of writing are 
more technical than others, and mathematics is a particularly technical 
form of writing.  Rod numerals functioned in the work of the Song/Yuan 
algebraists in the same way that algebraic notation does for a modern 
mathematician.  Thus for example, referring to the page from a 13th 
century book reproduced in Needham (1959) p. 132, I would translate the 
passage from the bottom of the fourth column from the right (reading 
right to left) roughly as:

" ... having done that, multiply the breadth of the yellow hypotenuse 
by the unknown, to obtain (-2x^2 + 654x), then divide that by ..."

The expression shown here using algebra is set out in the original 
using rod numerals.  If that is not writing, then algebra is not 
writing either. I revert again to the cross-cultural issue: why should 
modern western mathematicians have the privilege of finding everything 
they need in Unicode, whereas those who wish to write Chinese 
mathematics have to resort to pasting graphics into their texts, 
because someone decides that parts of those texts are not "real 
writing"?

Incidentally, I do note that provision has been made to encode the 64 
hexagrams of the Book of Change, and also the symbols used in Yang 
Xiong's Taixuan jing. See

http://www.unicode.org/charts/

under "Yi Jing hexagram symbols" and "Tai xuan jing symbols".  While I 
think that the idea of "writing" may not be in the last analysis a 
helpful one to use as a demarcation criterion for Unicode, given that 
the home page does say "The Unicode Standard defines codes for .... 
arrows, dingbats, etc.", I would think that if the hexagrams etc. are 
in, then a fortiori so should rod numerals be.  Much more if  the Tai 
xuan jing symbols are in, which I personally have never seen used 
outside the context of the ancient book in which they occur (maybe I'm 
just ignorant.  Yes, I probably am).

Christopher

On 13 Jan 2004, at 16:05, Marco Cimarosti wrote:

Christopher Cullen wrote:
(2) The Unicode home page says: "The Unicode Standard defines
codes for characters used in all the major languages [...]
mathematical symbols, technical symbols, [...]".
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.
I think that Ken Whistler point was simply this:

        OK, Chinese rod numerals may be symbols, but were these symbols used
in *writing*?
Not all symbols are used in writing, and only symbols used in writing 
are
suitable to be part of a repertoire of, well, encoding symbols used in
writing...

A flag, a medal, a tattoo, T-shirt may definitely be calle4d 
"symbols", yet
Unicode does not need a code point for "Union Jack" or "Che Guevara
T-Shirt".

To stick to mathematics, a pellet on an abacus, a key on an electronic
calculator, or a curve drawn on a whiteboard may legitimately be 
considered
symbols for numbers or other mathematical concepts. Yet, Unicode does 
not
need a code point for "abacus pellet", or "memory recall key", or 
"hyperbola
with horizontal axis", because these symbols are not elements of 
writing.

IMHO, in your proposal you should provide evidence that the answer to 
the
above question is "yes". I.e., you don't need to prove that these 
symbols
were used in Chinese mathematics, but rather that they were used to 
*write*
something (numbers, arguably, or arithmetical operations, etc.).

_ Marco