From: John Jenkins (jenkins@apple.com)
Date: Tue Jan 13 2004 - 11:47:58 EST
On Jan 12, 2004, at 6:45 PM, Kenneth Whistler wrote:
> 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*.
>
*sigh* You're just trying to make me dig out my copy of Needham,
aren't you?
The counting-rod forms are an outgrowth of (ultimately) oracle bone
forms (see Needham, vol. 3, pp. 6-7 for a chart). The forms for 1-4 on
the oracle bones pretty much match the later counting-rod forms, and by
the time of Zhou dynasty coinage, the forms for 5-9 do, as well. The
main difference between the Zhou coins and the counting rods is the use
of alternating orientations for different decimal places. Certainly,
then, these symbols are part of a family of symbols used to actually
represent numbers in earlier Chinese texts in a context separate from
diagrams. Unfortunately, the only actual copy of the Chinese
mathematical classics I've got is a fairly recent edition of the
Jiuzhang Suanshu, which was published in the PRC and actually uses
simplified forms throughout, so it's not a reliable indication of what
the text would originally have. My copy of Libbrecht seems to be AWOL.
I'll see if I can dig up a copy of the Sunzi Suanshu or any of the
works of the great Song mathematicians. (Oh, if only there were
somebody I knew with access to Berkeley's Far Eastern Library!)
Meanwhile, the point you raise is a fairly subtle one. I've seen
books, for example, with pictures of slide rules or abaci illustrating
their use. I think here, however, although there is in the mind of the
Chinese mathematicians an inextricable link between the two, it's
rather on the order of our using Arabic numerals on our calculators and
in our math books. That is, they not only used them to illustrate how
to uses the instruments, but also in tables of numerals with
mathematical interest. (E.g., the famous diagram of Pascal's triangle
in the Siyuan Yujian.)
========
John H. Jenkins
jenkins@apple.com
jhjenkins@mac.com
http://homepage..mac.com/jhjenkins/
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