From: leung@DSG.Tandem.COM (Steven Leung)
Subject: Re: Link bet'n math skill and linguistic characteristics
Originator: leung@bittemple
Organization: Tandem Computers
Date: Thu, 7 Jan 1993 17:25:27 GMT


zhang@csgrad.cs.vt.edu (Yaoen Zhang) writes:

> I have a question about the Math history of China.  I read a
> book called  "The Main Stream of World Civilization" a couple years
> back.  I remembered it mentioned that it was a milestone in
> science in Western Civilization to change from hexadecimal system 
> (base is 16) to decimal system (base 10).  The decimal system
> use Arab numbers (such as "0 1 2 ",which is actually invented in India).

It's not clear to me what you said "invented in India" refers to the
decimal system itself or the use of the Arab numbers as the symbols for
the 10 digits. For the former, that means India must have that established
earlier than us (see below), and I don't know much about that. For
the later, it's kind of strange. For if Arabs only have these 10 symbols
to construct a number, doesn't it mean that they have the decimal system
already? So that interpretation makes sense only if the Arabs have more
than 10 symbols (like english using eleven and twelve instead of ten-one
and ten-two to represent 11 and 12) and the Indians pick the ten out of
the whole set for use in the decimal system. I don't know much about it
either. (If A has the decimal system first, B has a good set of symbols,
and C select a subset from B to come up the same thing as A's system. Can
C claim to first invent this system of C's? In a very narrow sense, I guess
so. But it doesn't sound like a big deal to me.) I comment on this just
want the info/question be clarified.

> Recently I have been reading some ancient Chines articles.  I
> have found that people use decimal system in around 330 B.C.
> (about 2200 years back).  For example, fifty five (in Chinese,
> i.e., wu2 shi2 wu2).   
> 
> The question is wether our ancesters were using decimal system
> through out the known history of our civilization.

I do learn something about this magic number 55 lately. The earliest
record about this number appears to be in YiJing (the Book of Change)
and is called Tian(sky) Di(earth) Shu(number). It is called TDS because
it is the sum of Tian Shu (25) and Di Shu (30). Now, what are these
Tian Shu and Di Shu? Well, YJ, as all we know, primarily deals with the
concept of YinYang and its application. It classifies the odd digits
1,3,5,7,9 as Yang/Tian numbers and the even digits 2,4,6,8,10 as Yin/Di
numbers. The sums of these Tian/Di digits are 25 and 30, respectively.
Now, obviously, the numbers of 25, 30, and 55 clearly indicate that
the ancient folks in China already doing the decimal calculations. So,
if any other nation/race claim to have the decimal system first, they
need to show something earlier than this.

Furthermore, there are some references in YJ about the origin of this
system of numbering (I prefer to call it counting) as related to the
famous He(river) Tu(picture) and Luo(river_Luo) Shu(book). However, the
actual HeTu and LuoShu as what we see today actually appear after the
Song Dynasty. So, there are a lot of interpretations/speculations of
what this means.

I think our ancesters are pretty comfortable of doing additions in
decimal system. In Chinese translation, we call the decimal system as
Shi(ten) Jin(increment_the_next_digit?) system. And in this sense, we
we may be the earliest to develop the decimal system. But I think our
ancestors also appear to have some trouble in dealing with the concept 0.
This is indicated by the set of digits they called as Tian Shu and Di Shu:
they pick the ten instead of 0 together with the other nine to form sort of
the fundamental digit set. And another indication is that in YJ, it seems
to me that they use the binary representation of yin (--) and yang (__) to
construct number sets relatively easily but quite uneasy about how these
two representation come about from the first place and thus struggle a lot
on the concept of WuJi(void) and how this WuJi becomes TaiJi(singularity?)
which in turn gives birth to the Liang(2) Yi(?), i.e., yin and yang, etc.

Steven
-- 
328. Seek opportunity, not security. ...
        - Life's Little Instruction Book by H. J. Brown, Jr.

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