Re: Chinese rod numerals

From: Christopher Cullen (
Date: Tue Jan 13 2004 - 12:39:54 EST

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    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

    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

    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).


    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

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